The Grothendieck construction provides an explicit link between
indexed categories and opfibrations. It is a fundamental concept in
category theory and related fields with far reaching applications.
Bipermutative categories are categorifications of rings. They play
a central role in algebraic K-theory and infinite loop space
theory. This monograph is a detailed study of the Grothendieck
construction over a bipermutative category in the context of
categorically enriched multicategories, with new and important
applications to inverse K-theory and pseudo symmetric
E∞-algebras. After carefully recalling preliminaries in enriched
categories, bipermutative categories, and enriched multicategories,
we show that the Grothendieck construction over a small tight
bipermutative category is a pseudo symmetric Cat-multifunctor and
generally not a Cat-multifunctor in the symmetric sense. Pseudo
symmetry of Cat-multifunctors is a new concept we introduce in this
work. The following features make it accessible as a graduate text
or reference for experts: Complete definitions and proofs.
Self-contained background. Parts of Chapters 1–3, 7, 9, and 10
contain background material from the research literature. Extensive
cross-references. Connections between chapters. Each chapter has
its own introduction discussing not only the topics of that chapter
but also its connection with other chapters. Open questions.
Appendix A contains open questions that arise from the material in
the text and are suitable for graduate students. This book is
suitable for graduate students and researchers with an interest in
category theory, algebraic K-theory, homotopy theory, and related
fields. The presentation is thorough and self-contained, with
complete details and background material for non-expert readers.
General
| Imprint: |
Taylor & Francis
|
| Country of origin: |
United Kingdom |
| Release date: |
November 2023 |
| First published: |
2024 |
| Authors: |
Donald Yau
|
| Dimensions: |
234 x 156mm (L x W) |
| Pages: |
370 |
| ISBN-13: |
978-1-03-258404-1 |
| Categories: |
Books
|
| LSN: |
1-03-258404-1 |
| Barcode: |
9781032584041 |
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