Dominique Bourn's Books

Mal'cev, Protomodular, Homological and Semi-Abelian Categories

By: Francis Borceux,Dominique Bourn

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Mal'cev, Protomodular, Homological and Semi-Abelian Categories

By: Francis Borceux,Dominique Bourn

The purpose of the book is to take stock of the situation concerning Algebra via Category Theory in the last fifteen years, where the new and synthetic notions of Mal'cev, protomodular, homological and semi-abelian categories emerged. These notions force attention on the fibration of points and allow a unified treatment of the main algebraic: homological lemmas, Noether isomorphisms, commutator theory. The book gives full importance to examples and makes strong connections with Universal Algebra. One of its aims is to allow appreciating how productive the essential categorical constraint is: knowing an object, not from inside via its elements, but from outside via its relations with its environment. The book is intended to be a powerful tool in the hands of researchers in category theory, homology theory and universal algebra, as well as a textbook for graduate courses on these topics.

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Page Count

504

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402019610

ISBN 13

9781402019616

From Groups to Categorial Algebra

Introduction to Protomodular and Mal’tsev Categories

By: Dominique Bourn

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From Groups to Categorial Algebra

Introduction to Protomodular and Mal’tsev Categories

By: Dominique Bourn

This book gives a thorough and entirely self-contained, in-depth introduction to a specific approach to group theory, in a large sense of that word. The focus lie on the relationships which a group may have with other groups, via “universal properties”, a view on that group “from the outside”. This method of categorical algebra, is actually not limited to the study of groups alone, but applies equally well to other similar categories of algebraic objects. By introducing protomodular categories and Mal’tsev categories, which form a larger class, the structural properties of the category Gp of groups, show how they emerge from four very basic observations about the algebraic litteral calculus and how, studied for themselves at the conceptual categorical level, they lead to the main striking features of the category Gp of groups. Hardly any previous knowledge of category theory is assumed, and just a little experience with standard algebraic structures such as groups and monoids. Examples and exercises help understanding the basic definitions and results throughout the text.

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Page Count

113

Publisher

Birkhäuser

Published Date

ISBN 10

3319572199

ISBN 13

9783319572192

Shakespeare's Early History Plays

From Chronicle to Stage

By: Dominique Goy-Blanquet

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Shakespeare's Early History Plays

From Chronicle to Stage

By: Dominique Goy-Blanquet

Like many of his fellow playwrights, Shakespeare turned to national history for inspiration. In this study, Dominique Goy-Blanquet provides a close comparison of the Henry VI plays and Richard III with their historical and theatrical sources, demonstrating how Shakespeare was able to meet not only the ideological but also the technical problems of turning history into drama, how by cutting, carving, shaping, casting his unwieldy material into performable plays, he matured into the most influential dramatist and historian of his time. Recent criticism of Shakespeare's history plays has often consisted of fierce arguments over their ideological import and Shakespeare's position on the spectrum of current political opinions. This book, however, stems from the belief that a more constructive starting point for research is the exploration of the technical problems raised by turning heavy narratives into performable plays, rather than the political motives that could inpire a playwright's representation of national history. Illuminating and instructive, Shakespeare's Early History Plays includes not only close investigation of the verbal, poetic, and political texture of the plays, but also provides a broad overview of the wider sixteenth-century historiographical contexts of the plays, and their significance to Shakespeare's oeuvre more generally.

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