Enriched Categories, Internal Categories and Change of Base
Author : Dominic Verity
Publisher :
Page : pages
File Size : 32,33 MB
Release : 1992
Category :
ISBN :
Author : Dominic Verity
Publisher :
Page : pages
File Size : 32,33 MB
Release : 1992
Category :
ISBN :
Author : Gregory Maxwell Kelly
Publisher : CUP Archive
Page : 260 pages
File Size : 21,33 MB
Release : 1982-02-18
Category : Mathematics
ISBN : 9780521287029
Author : Ezra Getzler
Publisher : American Mathematical Soc.
Page : 146 pages
File Size : 10,65 MB
Release : 1998
Category : Mathematics
ISBN : 0821810561
Comprises six presentations on new developments in category theory from the March 1997 workshop. The topics are categorification, computads for finitary monads on globular sets, braided n- categories and a-structures, categories of vector bundles and Yang- Mills equations, the role of Michael Batanin's monoidal globular categories, and braided deformations of monoidal categories and Vassiliev invariants. No index. Annotation copyrighted by Book News, Inc., Portland, OR.
Author : Emily Riehl
Publisher : Cambridge University Press
Page : 781 pages
File Size : 47,64 MB
Release : 2022-02-10
Category : Mathematics
ISBN : 1108837980
This book develops the theory of infinite-dimensional categories by studying the universe, or ∞-cosmos, in which they live.
Author : Nick Gurski
Publisher : Cambridge University Press
Page : 287 pages
File Size : 12,21 MB
Release : 2013-03-21
Category : Mathematics
ISBN : 1107034892
Serves as an introduction to higher categories as well as a reference point for many key concepts in the field.
Author : Robert Andrew George Seely
Publisher : American Mathematical Soc.
Page : 462 pages
File Size : 48,17 MB
Release : 1992
Category : Mathematics
ISBN : 9780821860182
Representing this diversity of the field, this book contains the proceedings of an international conference on category theory. The subjects covered here range from topology and geometry to logic and theoretical computer science, from homotopy to braids and conformal field theory. Although generally aimed at experts in the various fields represented, the book will also provide an excellent opportunity for nonexperts to get a feel for the diversity of current applications of category theory.
Author : Emily Riehl
Publisher : Cambridge University Press
Page : 371 pages
File Size : 16,27 MB
Release : 2014-05-26
Category : Mathematics
ISBN : 1107048451
This categorical perspective on homotopy theory helps consolidate and simplify one's understanding of derived functors, homotopy limits and colimits, and model categories, among others.
Author : Emily Riehl
Publisher : Cambridge University Press
Page : 782 pages
File Size : 50,84 MB
Release : 2022-02-10
Category : Mathematics
ISBN : 1108952194
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 : Emily Riehl
Publisher : Cambridge University Press
Page : 371 pages
File Size : 15,80 MB
Release : 2014-05-26
Category : Mathematics
ISBN : 1139952633
This book develops abstract homotopy theory from the categorical perspective with a particular focus on examples. Part I discusses two competing perspectives by which one typically first encounters homotopy (co)limits: either as derived functors definable when the appropriate diagram categories admit a compatible model structure, or through particular formulae that give the right notion in certain examples. Emily Riehl unifies these seemingly rival perspectives and demonstrates that model structures on diagram categories are irrelevant. Homotopy (co)limits are explained to be a special case of weighted (co)limits, a foundational topic in enriched category theory. In Part II, Riehl further examines this topic, separating categorical arguments from homotopical ones. Part III treats the most ubiquitous axiomatic framework for homotopy theory - Quillen's model categories. Here, Riehl simplifies familiar model categorical lemmas and definitions by focusing on weak factorization systems. Part IV introduces quasi-categories and homotopy coherence.
Author : Javier Esparza
Publisher : Springer
Page : 571 pages
File Size : 20,71 MB
Release : 2017-03-15
Category : Computers
ISBN : 366254458X
This book constitutes the proceedings of the 20th International Conference on Foundations of Software Science and Computation Structures, FOSSACS 2017, which took place in Uppsala, Sweden in April 2017, held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2017. The 32 papers presented in this volume were carefully reviewed and selected from 101 submissions. They were organized in topical sections named: coherence spaces and higher-order computation; algebra and coalgebra; games and automata; automata, logic and formal languages; proof theory; probability; concurrency; lambda calculus and constructive proof; and semantics and category theory.