Kan Extensions in Enriched Category Theory PDF Download

Author: Eduardo J. Dubuc
Publisher: Springer
ISBN: 3540363076
Category : Mathematics
Languages : en
Pages : 190

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Book Description
The original purpose of this paper was to provide suitable enriched completions of small enriched categories.

Author: Gregory Maxwell Kelly
Publisher: CUP Archive
ISBN: 9780521287029
Category : Mathematics
Languages : en
Pages : 260

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Book Description

Author: Fosco Loregian
Publisher: Cambridge University Press
ISBN: 1108746128
Category : Mathematics
Languages : en
Pages : 331

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Book Description
This easy-to-cite handbook gives the first systematic treatment of the (co)end calculus in category theory and its applications.

Author: Tom Leinster
Publisher: Cambridge University Press
ISBN: 1107044243
Category : Mathematics
Languages : en
Pages : 193

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Book Description
A short introduction ideal for students learning category theory for the first time.

Author: Birgit Richter
Publisher: Cambridge University Press
ISBN: 1108847625
Category : Mathematics
Languages : en
Pages : 402

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Book Description
Category theory provides structure for the mathematical world and is seen everywhere in modern mathematics. With this book, the author bridges the gap between pure category theory and its numerous applications in homotopy theory, providing the necessary background information to make the subject accessible to graduate students or researchers with a background in algebraic topology and algebra. The reader is first introduced to category theory, starting with basic definitions and concepts before progressing to more advanced themes. Concrete examples and exercises illustrate the topics, ranging from colimits to constructions such as the Day convolution product. Part II covers important applications of category theory, giving a thorough introduction to simplicial objects including an account of quasi-categories and Segal sets. Diagram categories play a central role throughout the book, giving rise to models of iterated loop spaces, and feature prominently in functor homology and homology of small categories.

Author: Emily Riehl
Publisher: Courier Dover Publications
ISBN: 0486820807
Category : Mathematics
Languages : en
Pages : 273

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Book Description
Introduction to concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions, monads — revisits a broad range of mathematical examples from the categorical perspective. 2016 edition.

Author: Emily Riehl
Publisher: Cambridge University Press
ISBN: 1108952194
Category : Mathematics
Languages : en
Pages : 782

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Book Description
The language of ∞-categories provides an insightful new way of expressing many results in higher-dimensional mathematics but can be challenging for the uninitiated. To explain what exactly an ∞-category is requires various technical models, raising the question of how they might be compared. To overcome this, a model-independent approach is desired, so that theorems proven with any model would apply to them all. This text develops the theory of ∞-categories from first principles in a model-independent fashion using the axiomatic framework of an ∞-cosmos, the universe in which ∞-categories live as objects. An ∞-cosmos is a fertile setting for the formal category theory of ∞-categories, and in this way the foundational proofs in ∞-category theory closely resemble the classical foundations of ordinary category theory. Equipped with exercises and appendices with background material, this first introduction is meant for students and researchers who have a strong foundation in classical 1-category theory.

Author: Bartosz Milewski
Publisher:
ISBN: 9780464243878
Category :
Languages : en
Pages :

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Book Description
Category Theory is one of the most abstract branches of mathematics. It is usually taught to graduate students after they have mastered several other branches of mathematics, like algebra, topology, and group theory. It might, therefore, come as a shock that the basic concepts of category theory can be explained in relatively simple terms to anybody with some experience in programming.That's because, just like programming, category theory is about structure. Mathematicians discover structure in mathematical theories, programmers discover structure in computer programs. Well-structured programs are easier to understand and maintain and are less likely to contain bugs. Category theory provides the language to talk about structure and learning it will make you a better programmer.

Author: Brendan Fong
Publisher: Cambridge University Press
ISBN: 1108482295
Category : Computers
Languages : en
Pages : 351

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Book Description
Category theory reveals commonalities between structures of all sorts. This book shows its potential in science, engineering, and beyond.

Author: Jacob Lurie
Publisher: Princeton University Press
ISBN: 1400830559
Category : Mathematics
Languages : en
Pages : 944

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Book Description
Higher category theory is generally regarded as technical and forbidding, but part of it is considerably more tractable: the theory of infinity-categories, higher categories in which all higher morphisms are assumed to be invertible. In Higher Topos Theory, Jacob Lurie presents the foundations of this theory, using the language of weak Kan complexes introduced by Boardman and Vogt, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language. The result is a powerful theory with applications in many areas of mathematics. The book's first five chapters give an exposition of the theory of infinity-categories that emphasizes their role as a generalization of ordinary categories. Many of the fundamental ideas from classical category theory are generalized to the infinity-categorical setting, such as limits and colimits, adjoint functors, ind-objects and pro-objects, locally accessible and presentable categories, Grothendieck fibrations, presheaves, and Yoneda's lemma. A sixth chapter presents an infinity-categorical version of the theory of Grothendieck topoi, introducing the notion of an infinity-topos, an infinity-category that resembles the infinity-category of topological spaces in the sense that it satisfies certain axioms that codify some of the basic principles of algebraic topology. A seventh and final chapter presents applications that illustrate connections between the theory of higher topoi and ideas from classical topology.