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Bimonoidal Categories, En-Monoidal Categories, and Algebraic K-Theory (The Set): Volumes I...
出版済み 3-5週間でお届けいたします。
Author: Donald Yau, Niles Johnson Publisher: American Mathematical Society ISBN: 9781470479411 Cover: PAPERBACK Date: 2024年11月 DESCRIPTION Volume I: Symmetric Bimonoidal Categories and Monoidal Bicategories Volume II: Braided Bimonoidal Categories with Applications Volume III: From Categories to Structured Ring Spectra Bimonoidal categories are categorical analogues of rings without additive inverses. They have been actively studied in category theory, homotopy theory, and algebraic K -theory since around 1970. There is an abundance of new applications and questions of bimonoidal categories in mathematics and other sciences. The three books published by the AMS in the Mathematical Surveys and Monographs series under the general title Bimonoidal Categories, En -Monoidal Categories, and Algebraic K -Theory (Volume I: Symmetric Bimonoidal Categories and Monoidal Bicategories, Volume II: Braided Bimonoidal Categories with Applications, and Volume III: From Categories to Structured Ring Spectra) provide a unified treatment of bimonoidal and higher ring-like categories, their connection with algebraic K -theory and homotopy theory, and applications to quantum groups and topological quantum computation. With ample background material, extensive coverage, detailed presentation of both well-known and new theorems, and a list of open questions, this work is a user-friendly resource for beginners and experts alike. TABLE OF CONTENTS Volume I: Symmetric Bimonoidal Categories and Monoidal Bicategories Symmetric bimonoidal categories Basic category theory Symmetric bimonoidal categories Coherence of symmetric bimonoidal categories Coherence of symmetric bimonoidal categories II Strictification of tight symmetric bimonoidal categories Bicategorical aspects of symmetric bimonoidal categories Definitions from bicategory theory Baez’s conjecture Symmetric monoidal bicategorification Volume II: Braided Bimonoidal Categories with Applications Braided bimonoidal categories Preliminaries on braided structures Braided bimonoidal categories Applications to quantum groups and topological quantum computation Bimonoidal centers Coherence of braided bimonoidal categories Strictification of tight braided bimonoidal categories The braided Baez conjecture Monoidal bicategorification En -monoidal categories Ring, bipermutative, and braided ring categories Iterated and En -monoidal categories Volume III: From Categories to Structured Ring Spectra Enriched monoidal categories and multicategories Enriched monoidal categories Change of enrichment Self-enrichment and enriched Yoneda Pointed objects, smash products, and pointed homs Multicategories Enriched multicategories Algebraic K -theory Homotopy theory background Segal K -theory of permutative categories Categories of G? -objects Elmendorf-Mandell K -theory of permutative categories K -theory of ring and bipermutative categories K -theory of braided ring categories K -theory of En -monoidal categories
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