Grothendieck Construction of Bipermutative-Indexed Categories

The Grothendieck construction is a fundamental concept in category theory and related fields, providing an explicit link between indexed categories and opfibrations. This monograph studies the Grothendieck construction over a bipermutative category in the context of categorically enriched multicategories, with new applications to inverse K-theory and pseudo symmetric E∞-algebras. It is accessible as a graduate text or reference for experts, with complete definitions, proofs, background material, cross-references, and open questions.

Format: Hardback
Length: 330 pages
Publication date: 06 December 2023
Publisher: Taylor & Francis Ltd

The Grothendieck construction is a groundbreaking concept that establishes a profound connection between indexed categories and opfibrations, playing a central role in category theory and its related fields. Bipermutative categories, a specialized form of categorizations, are particularly significant in algebraic K-theory and infinite loop space theory. In this comprehensive monograph, we delve into the Grothendieck construction over a bipermutative category within the framework of categorically enriched multicategories. We explore new and exciting applications to inverse K-theory and pseudo symmetric E∞-algebras.

To provide a solid foundation, we begin by reviewing preliminaries in enriched categories, bipermutative categories, and enriched multicategories. We then demonstrate that the Grothendieck construction over a small tight bipermutative category is a pseudo symmetric Cat-multifunctor, which is a novel concept introduced in this work. Pseudo symmetry of Cat-multifunctors offers a fresh perspective on the construction.

This book is designed to serve as a valuable resource for graduate students and researchers with a deep interest in category theory, algebraic K-theory, homotopy theory, and related fields. The presentation is thorough and self-contained, offering complete definitions and proofs, as well as a self-contained background that includes material from the research literature. Extensive cross-references and connections between chapters facilitate a seamless understanding of the subject matter. Additionally, Appendix A contains open questions that challenge readers and encourage further exploration.

With its comprehensive coverage and accessible style, this book is an ideal choice for advanced students and scholars seeking to delve into the intricate world of category theory and its applications.

Weight: 816g
Dimension: 234 x 156 (mm)
ISBN-13: 9781032584041