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Softcover ISBN:  9781470478094 
Product Code:  SURV/283 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
eBook ISBN:  9781470478469 
Product Code:  SURV/283.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9781470478094 
eBook ISBN:  9781470478469 
Product Code:  SURV/283.B 
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AMS Member Price:  $208.00 $158.00 

Book DetailsMathematical Surveys and MonographsVolume: 283; 2024; 520 ppMSC: Primary 18; 19; 55
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, \(E_n\)Monoidal Categories, and Algebraic \(K\)Theory (Volume I: Symmetric Bimonoidal Categories and Monoidal Bicategories—this book, Volume II: Braided Bimonoidal Categories with Applications, and Volume III: From Categories to Structured Ring Spectra) provide a unified treatment of bimonoidal and higher ringlike 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 wellknown and new theorems, and a list of open questions, this work is a userfriendly resource for beginners and experts alike.
Part 1 of this book proves in detail Laplaza's two coherence theorems and May's strictification theorem of symmetric bimonoidal categories, as well as their bimonoidal analogues. This part includes detailed corrections to several inaccurate statements and proofs found in the literature. Part 2 proves Baez's Conjecture on the existence of a biinitial object in a 2category of symmetric bimonoidal categories. The next main theorem states that a matrix construction, involving the matrix product and the matrix tensor product, sends a symmetric bimonoidal category with invertible distributivity morphisms to a symmetric monoidal bicategory, with no strict structure morphisms in general.
ReadershipGraduate students and researchers interested in category theory and algebraic \(K\)theory.
This item is also available as part of a set: 
Table of Contents

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

Bibliography and indices

Open questions

Bibliography

List of main facts

List of notations

Index


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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, \(E_n\)Monoidal Categories, and Algebraic \(K\)Theory (Volume I: Symmetric Bimonoidal Categories and Monoidal Bicategories—this book, Volume II: Braided Bimonoidal Categories with Applications, and Volume III: From Categories to Structured Ring Spectra) provide a unified treatment of bimonoidal and higher ringlike 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 wellknown and new theorems, and a list of open questions, this work is a userfriendly resource for beginners and experts alike.
Part 1 of this book proves in detail Laplaza's two coherence theorems and May's strictification theorem of symmetric bimonoidal categories, as well as their bimonoidal analogues. This part includes detailed corrections to several inaccurate statements and proofs found in the literature. Part 2 proves Baez's Conjecture on the existence of a biinitial object in a 2category of symmetric bimonoidal categories. The next main theorem states that a matrix construction, involving the matrix product and the matrix tensor product, sends a symmetric bimonoidal category with invertible distributivity morphisms to a symmetric monoidal bicategory, with no strict structure morphisms in general.
Graduate students and researchers interested in category theory and algebraic \(K\)theory.

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

Bibliography and indices

Open questions

Bibliography

List of main facts

List of notations

Index