Marco Grandis's Books

Category Theory And Applications: A Textbook For Beginners (Second Edition)

By: Marco Grandis

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Category Theory And Applications: A Textbook For Beginners (Second Edition)

By: Marco Grandis

Category Theory now permeates most of Mathematics, large parts of theoretical Computer Science and parts of theoretical Physics. Its unifying power brings together different branches, and leads to a better understanding of their roots.This book is addressed to students and researchers of these fields and can be used as a text for a first course in Category Theory. It covers the basic tools, like universal properties, limits, adjoint functors and monads. These are presented in a concrete way, starting from examples and exercises taken from elementary Algebra, Lattice Theory and Topology, then developing the theory together with new exercises and applications.A reader should have some elementary knowledge of these three subjects, or at least two of them, in order to be able to follow the main examples, appreciate the unifying power of the categorical approach, and discover the subterranean links brought to light and formalised by this perspective.Applications of Category Theory form a vast and differentiated domain. This book wants to present the basic applications in Algebra and Topology, with a choice of more advanced ones, based on the interests of the author. References are given for applications in many other fields.In this second edition, the book has been entirely reviewed, adding many applications and exercises. All non-obvious exercises have now a solution (or a reference, in the case of an advanced topic); solutions are now collected in the last chapter.

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390

Publisher

World Scientific

Published Date

ISBN 10

9811236100

ISBN 13

9789811236105

Homological Algebra

The Interplay of Homology with Distributive Lattices and Orthodox Semigroups

By: Marco Grandis

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Homological Algebra

The Interplay of Homology with Distributive Lattices and Orthodox Semigroups

By: Marco Grandis

In this book we want to explore aspects of coherence in homological algebra, that already appear in the classical situation of abelian groups or abelian categories. Lattices of subobjects are shown to play an important role in the study of homological systems, from simple chain complexes to all the structures that give rise to spectral sequences. A parallel role is played by semigroups of endorelations. These links rest on the fact that many such systems, but not all of them, live in distributive sublattices of the modular lattices of subobjects of the system. The property of distributivity allows one to work with induced morphisms in an automatically consistent way, as we prove in a 'Coherence Theorem for homological algebra'. (On the contrary, a 'non-distributive' homological structure like the bifiltered chain complex can easily lead to inconsistency, if one explores the interaction of its two spectral sequences farther than it is normally done.) The same property of distributivity also permits representations of homological structures by means of sets and lattices of subsets, yielding a precise foundation for the heuristic tool of Zeeman diagrams as universal models of spectral sequences. We thus establish an effective method of working with spectral sequences, called 'crossword chasing', that can often replace the usual complicated algebraic tools and be of much help to readers that want to apply spectral sequences in any field.

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382

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World Scientific

Published Date

ISBN 10

9814407070

ISBN 13

9789814407076

Algebraic Topology: A Structural Introduction

By: Marco Grandis

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Algebraic Topology: A Structural Introduction

By: Marco Grandis

Algebraic Topology is a system and strategy of partial translations, aiming to reduce difficult topological problems to algebraic facts that can be more easily solved. The main subject of this book is singular homology, the simplest of these translations. Studying this theory and its applications, we also investigate its underlying structural layout - the topics of Homological Algebra, Homotopy Theory and Category Theory which occur in its foundation.This book is an introduction to a complex domain, with references to its advanced parts and ramifications. It is written with a moderate amount of prerequisites — basic general topology and little else — and a moderate progression starting from a very elementary beginning. A consistent part of the exposition is organised in the form of exercises, with suitable hints and solutions.It can be used as a textbook for a semester course or self-study, and a guidebook for further study.

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372

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World Scientific

Published Date

ISBN 10

9811248370

ISBN 13

9789811248375

Environmental Standards

Combined Exposures and Their Effects on Human Beings and Their Environment

By: Christian Streffer,Josef Bücker,Adrienne Cansier,Dieter Cansier,Carl Friedrich Gethmann,Robert Guderian,Gerd Hanekamp,Dietrich Henschler,Gerald Pöch,Eckard Rehbinder,Ortwin Renn,Marco Slesina,Kerstin Wuttke

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Environmental Standards

Combined Exposures and Their Effects on Human Beings and Their Environment

The rapid growth of the world population - nearly six-fold over the last hundred years - combined with the rising number of technical installations especially in the industrialized countries has lead to ever tighter and more strained living spaces on our planet. Because ofthe inevitable processes oflife, man was at first an exploiter rather than a careful preserver of the environment. Environmental awareness with the intention to conserve the environment has grown only in the last few decades. Environmental standards have been defined and limit values have been set largely guided, however, by scientific and medical data on single exposures, while public opinion, on the other hand, now increasingly calls for astronger consideration of the more complex situations following combined exposures. Furthermore, it turned out that environmental standards, while necessarily based on scientific data, must also take into account ethical, legal, economic, and sociological aspects. A task of such complexity can only be dealt with appropriately in the framework of an inter disciplinary group.

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862

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540440976

ISBN 13

9783540440970

Gromov’s Theory of Multicomplexes with Applications to Bounded Cohomology and Simplicial Volume

By: Roberto Frigerio,Marco Moraschini

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Gromov’s Theory of Multicomplexes with Applications to Bounded Cohomology and Simplicial Volume

By: Roberto Frigerio,Marco Moraschini

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166

Publisher

American Mathematical Society

Published Date

ISBN 10

1470459914

ISBN 13

9781470459918

Principles and concepts for development in nowadays society

By: Mauro Pinho,Marco Antonio Schueda,Danielle do Rocio Brostulin

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Principles and concepts for development in nowadays society

By: Mauro Pinho,Marco Antonio Schueda,Danielle do Rocio Brostulin

Temos o prazer de lançar o primeiro livro internacional do ano de 2022 voltado a área do desenvolvimento, que tem como título Principles and concepts for development in nowadays society, essa obra contém 152 artigos voltados a área multidisciplinar, sendo a mesma pela Seven Publicações Ltda. A Seven Editora, agradece e enaltasse os autores que fizeram parte desse livro. Desejamos uma boa leitura a todos

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1915

Publisher

Seven Editora

ISBN 13

9798218077921

Sampling Methods, Remote Sensing and GIS Multiresource Forest Inventory

By: Michael Köhl,Steen S. Magnussen,Marco Marchetti

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Sampling Methods, Remote Sensing and GIS Multiresource Forest Inventory

By: Michael Köhl,Steen S. Magnussen,Marco Marchetti

This book presents the state-of-the-art of forest resources assessments and monitoring. It provides links to practical applications of forest and natural resource assessment programs. It offers an overview of current forest inventory systems and discusses forest mensuration, sampling techniques, remote sensing applications, geographic and forest information systems, and multi-resource forest inventory. Attention is also given to the quantification of non-wood goods and services.

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388

Publisher

Springer Science & Business Media

Published Date

ISBN 10

3540325727

ISBN 13

9783540325727

A Naturalist's Guide to the Tropics

By: Marco Lambertini

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A Naturalist's Guide to the Tropics

By: Marco Lambertini

Beautifully illustrated throughout with color plates, photographs, and drawings, this volume is a comprehensive introduction to the natural history of the tropics worldwide. 59 color photos. 21 maps.

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338

Publisher

University of Chicago Press

Published Date

ISBN 10

0226468283

ISBN 13

9780226468280

A Commentary on the Letters of M. Cornelius Fronto

By: Michael Petrus Josephus Van Den Hout,Marco Cornelio Frontón

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A Commentary on the Letters of M. Cornelius Fronto

By: Michael Petrus Josephus Van Den Hout,Marco Cornelio Frontón

This is the first commentary on the letters of Marcus Cornelius Fronto (c. 90-95 - c. 167). It aims at an extensive grammatical, stylistic and historical interpretation of the letters and the ancient testimonies on Fronto. The author demonstrates where he stands in Latin literature; hence the numerous quotations of parallel, similar and dissentient passages from Fronto and other writers. This commentary, based on the Teubner-edition by the author (Leipzig 1988), offers a thorough explanation of the letters, a close examination of Fronto's style and language, e.g., of his archaisms and colloquialisms, identification of the persons mentioned, and the chronology of the letters. Seven elaborate indices complete this book.

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752

Publisher

BRILL

Published Date

ISBN 10

9004109579

ISBN 13

9789004109575

Medieval Teachers of Freedom

Boethius, Peter Lombard and Aquinas on Creation from Nothing

By: Marco Antonio Andreacchio

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Medieval Teachers of Freedom

Boethius, Peter Lombard and Aquinas on Creation from Nothing

By: Marco Antonio Andreacchio

Medieval debates over "divine creation" are systematically obscured in our age by the conflict between "Intelligent Design" Creationists and Evolutionists. The present investigation cuts through the web of contemporary conflicts to examine problems seated at the heart of medieval talk about creation. From three representative authors we learn that the doctrine of divine creation is supposed to invite understanding of the relation between artistic freedom and natural necessity, of the very essence of causality, and thereby of the nexus between experience (our world of empirical determinations) and reality (the absolute indetermination of eternal being). Most importantly, medieval scholarship shows us that the problems it addresses are originally inherent in the understanding itself, whereby the question of being emerges as inseparable from the question of interpretation.

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Page Count

134

Publisher

Taylor & Francis

Published Date

ISBN 10

1000911543

ISBN 13

9781000911541

The Italian Mind

Vernacular Logic in Renaissance Italy (1540-1551)

By: Marco Sgarbi

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The Italian Mind

Vernacular Logic in Renaissance Italy (1540-1551)

By: Marco Sgarbi

From the twelfth to the seventeenth century, Aristotle’s writings lay at the foundation of Western culture, providing a body of knowledge and a set of analytical tools applicable to all areas of human investigation. Scholars of the Renaissance have emphasized the remarkable longevity and versatility of Aristotelianism, but they have mainly focused on the Latin tradition. Scarce, if any, attention has gone to vernacular works. Nonetheless, several important Renaissance figures wished to make Aristotle’s works accessible and available outside the narrow circle of professional philosophers and university professors to a broad set of readers. The thesis underpinning this book is that Italian vernacular Aristotelianism, especially in the field of logic, made fundamental contributions to the thought of the period, anticipating many of the features of early modern philosophy and contributing to a new conception of knowledge.

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256

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BRILL

Published Date

ISBN 10

9004264299

ISBN 13

9789004264298

Maxima culpa

By: Marco Nundini

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Maxima culpa

By: Marco Nundini

In una Verona letargica per il caldo estivo, Loreta Assensi, giovane ispettore di polizia, indaga su alcuni strani episodi accaduti tra le boscose colline che sovrastano la città scaligera: ragazzate e nulla più secondo i suoi superiori. Nessuno sospetta quanto la sensuale investigatrice sta per scoprire. Un brutale omicidio macchia di sangue i sentieri che corrono tra le ville della Verona bene, un'ombra maligna che serpeggia tra i pini ed i cipressi delle Torricelle. Lassù, dove lo sguardo abbraccia un panorama fatto di campanili, croci e santità, la fede di un'intera comunità parrocchiale vacilla alle lusinghe del peccato e nasconde verità inconfessabili tra le pieghe della devozione. Un'indagine senza respiro che, tra piste internazionali e mitologiche visioni di un oriente biblico, racconta l'eterna lotta tra il bene ed il male.

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333

Publisher

Marco Nundini/ilFilografo

Published Date

ISBN 10

8890870443

ISBN 13

9788890870446

Directed Algebraic Topology

Models of Non-Reversible Worlds

By: Marco Grandis

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Directed Algebraic Topology

Models of Non-Reversible Worlds

By: Marco Grandis

This is the first authored book to be dedicated to the new field of directed algebraic topology that arose in the 1990s, in homotopy theory and in the theory of concurrent processes. Its general aim can be stated as 'modelling non-reversible phenomena' and its domain should be distinguished from that of classical algebraic topology by the principle that directed spaces have privileged directions and directed paths therein need not be reversible. Its homotopical tools (corresponding in the classical case to ordinary homotopies, fundamental group and fundamental groupoid) should be similarly 'non-reversible': directed homotopies, fundamental monoid and fundamental category. Homotopy constructions occur here in a directed version, which gives rise to new 'shapes', like directed cones and directed spheres. Applications will deal with domains where privileged directions appear, including rewrite systems, traffic networks and biological systems. The most developed examples can be found in the area of concurrency.

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445

Publisher

Cambridge University Press

Published Date

ISBN 10

1139482580

ISBN 13

9781139482585

Higher Dimensional Categories: From Double To Multiple Categories

By: Marco Grandis

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Higher Dimensional Categories: From Double To Multiple Categories

By: Marco Grandis

The study of higher dimensional categories has mostly been developed in the globular form of 2-categories, n-categories, omega-categories and their weak versions. Here we study a different form: double categories, n-tuple categories and multiple categories, with their weak and lax versions.We want to show the advantages of this form for the theory of adjunctions and limits. Furthermore, this form is much simpler in higher dimension, starting with dimension three where weak 3-categories (also called tricategories) are already quite complicated, much more than weak or lax triple categories.This book can be used as a textbook for graduate and postgraduate studies, and as a basis for research. Notions are presented in a 'concrete' way, with examples and exercises; the latter are endowed with a solution or hints. Part I, devoted to double categories, starts at basic category theory and is kept at a relatively simple level. Part II, on multiple categories, can be used independently by a reader acquainted with 2-dimensional categories.

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535

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World Scientific

Published Date

ISBN 10

9811205124

ISBN 13

9789811205125

Algebraic Topology: A Structural Introduction

By: Marco Grandis

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Algebraic Topology: A Structural Introduction

By: Marco Grandis

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372

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World Scientific

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ISBN 10

9811248370

ISBN 13

9789811248375

Homological Algebra

In Strongly Non-Abelian Settings

By: Marco Grandis

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Homological Algebra

In Strongly Non-Abelian Settings

By: Marco Grandis

This book proposes a study of semi-exact homological categories as a basis for a generalized homological algebra. The aim is to extend homological notions to deeply non-abelian situations, where satellites and spectral sequences produced by unstable homotopy can still be studied.

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356

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World Scientific

Published Date

ISBN 10

9814425923

ISBN 13

9789814425926

Category Theory And Applications: A Textbook For Beginners

By: Marco Grandis

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Category Theory And Applications: A Textbook For Beginners

By: Marco Grandis

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305

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World Scientific

Published Date

ISBN 10

9813231084

ISBN 13

9789813231085

Elementary Overview Of Mathematical Structures, An: Algebra, Topology And Categories

By: Marco Grandis

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Elementary Overview Of Mathematical Structures, An: Algebra, Topology And Categories

By: Marco Grandis

The presentation is modeled on the discursive style of the Bourbaki collective, and the coverage of topics is rich and varied. Grandis has provided a large selection of exercises and has sprinkled orienting comments throughout. For an undergraduate library where strong students seek an overview of a significant portion of mathematics, this would be an excellent acquisition. Summing up: Recommended.'CHOICESince the last century, a large part of Mathematics is concerned with the study of mathematical structures, from groups to fields and vector spaces, from lattices to Boolean algebras, from metric spaces to topological spaces, from topological groups to Banach spaces.More recently, these structured sets and their transformations have been assembled in higher structures, called categories.We want to give a structural overview of these topics, where the basic facts of the different theories are unified through the 'universal properties' that they satisfy, and their particularities stand out, perhaps even more.This book can be used as a textbook for undergraduate studies and for self-study. It can provide students of Mathematics with a unified perspective of subjects which are often kept apart. It is also addressed to students and researchers of disciplines having strong interactions with Mathematics, like Physics and Chemistry, Statistics, Computer Science, Engineering.

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393

Publisher

World Scientific

Published Date

ISBN 10

9811220336

ISBN 13

9789811220333

Homological Algebra: The Interplay Of Homology With Distributive Lattices And Orthodox Semigroups

By: Marco Grandis

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Homological Algebra: The Interplay Of Homology With Distributive Lattices And Orthodox Semigroups

By: Marco Grandis

In this book we want to explore aspects of coherence in homological algebra, that already appear in the classical situation of abelian groups or abelian categories. Lattices of subobjects are shown to play an important role in the study of homological systems, from simple chain complexes to all the structures that give rise to spectral sequences. A parallel role is played by semigroups of endorelations.These links rest on the fact that many such systems, but not all of them, live in distributive sublattices of the modular lattices of subobjects of the system.The property of distributivity allows one to work with induced morphisms in an automatically consistent way, as we prove in a ‘Coherence Theorem for homological algebra’. (On the contrary, a ‘non-distributive’ homological structure like the bifiltered chain complex can easily lead to inconsistency, if one explores the interaction of its two spectral sequences farther than it is normally done.)The same property of distributivity also permits representations of homological structures by means of sets and lattices of subsets, yielding a precise foundation for the heuristic tool of Zeeman diagrams as universal models of spectral sequences.We thus establish an effective method of working with spectral sequences, called ‘crossword chasing’, that can often replace the usual complicated algebraic tools and be of much help to readers that want to apply spectral sequences in any field.

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Page Count

382

Publisher

World Scientific

Published Date

ISBN 10

9814407089

ISBN 13

9789814407083

Higher Dimensional Categories: From Double To Multiple Categories

By: Marco Grandis

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Higher Dimensional Categories: From Double To Multiple Categories

By: Marco Grandis

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535

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World Scientific

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ISBN 10

9811205124

ISBN 13

9789811205125

Manifolds And Local Structures: A General Theory

By: Marco Grandis

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Manifolds And Local Structures: A General Theory

By: Marco Grandis

Local structures, like differentiable manifolds, fibre bundles, vector bundles and foliations, can be obtained by gluing together a family of suitable 'elementary spaces', by means of partial homeomorphisms that fix the gluing conditions and form a sort of 'intrinsic atlas', instead of the more usual system of charts living in an external framework.An 'intrinsic manifold' is defined here as such an atlas, in a suitable category of elementary spaces: open euclidean spaces, or trivial bundles, or trivial vector bundles, and so on.This uniform approach allows us to move from one basis to another: for instance, the elementary tangent bundle of an open Euclidean space is automatically extended to the tangent bundle of any differentiable manifold. The same holds for tensor calculus.Technically, the goal of this book is to treat these structures as 'symmetric enriched categories' over a suitable basis, generally an ordered category of partial mappings.This approach to gluing structures is related to Ehresmann's one, based on inductive pseudogroups and inductive categories. A second source was the theory of enriched categories and Lawvere's unusual view of interesting mathematical structures as categories enriched over a suitable basis.

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Page Count

374

Publisher

World Scientific

Published Date

ISBN 10

9811234019

ISBN 13

9789811234019

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