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The cohomology of monoids

Record Type:	Electronic resources : Monograph/item
Title/Author:	The cohomology of monoidsby Antonio M. Cegarra, Jonathan Leech.
Author:	Cegarra, Antonio M.
other author:	Leech, Jonathan.
Published:	Cham :Springer Nature Switzerland :2024.
Description:	xiv, 214 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Cohomology operations.
Online resource:	https://doi.org/10.1007/978-3-031-50258-3
ISBN:	9783031502583$q(electronic bk.)

The cohomology of monoids
Cegarra, Antonio M.

The cohomology of monoids[electronic resource] /by Antonio M. Cegarra, Jonathan Leech. - Cham :Springer Nature Switzerland :2024. - xiv, 214 p. :ill., digital ;24 cm. - RSME Springer series,v. 122509-8896 ;. - RSME Springer series ;v.1..

This monograph covers topics in the cohomology of monoids up through recent developments. Jonathan Leech's original monograph in the Memoirs of the American Mathematical Society dates back to 1975. This book is an organized, accessible, and self-contained account of this cohomology that includes more recent significant developments that were previously scattered among various publications, along with completely new material. It summarizes the original Leech theory and provides a modern and thorough treatment of the cohomological classification of coextensions of both monoids and monoidal groupoids, including the case of monoids with operators. This cohomology is also compared to the classical Eilenberg-Mac Lane and Hochschild-Mitchell cohomologies. Connections are also established with the Lausch-Loganathan cohomology theory for inverse semigroups, the Gabriel-Zisman cohomology of simplicial sets, the Wells cohomology of small categories (also known as Baues-Wirsching cohomology), Grothendieck sheaf cohomology, and finally Beck's triple cohomology. It also establishes connections with Grillet's cohomology theory for commutative semigroups. The monograph is aimed at researchers in the theory of monoids, or even semigroups, and its interface with category theory, homological algebra, and related fields. However, it is also written to be accessible to graduate students in mathematics and mathematicians in general.

ISBN: 9783031502583$q(electronic bk.)

Standard No.: 10.1007/978-3-031-50258-3doiSubjects--Topical Terms:

348598
Cohomology operations.

LC Class. No.: QA169

Dewey Class. No.: 514.23

The cohomology of monoids
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520 $a This monograph covers topics in the cohomology of monoids up through recent developments. Jonathan Leech's original monograph in the Memoirs of the American Mathematical Society dates back to 1975. This book is an organized, accessible, and self-contained account of this cohomology that includes more recent significant developments that were previously scattered among various publications, along with completely new material. It summarizes the original Leech theory and provides a modern and thorough treatment of the cohomological classification of coextensions of both monoids and monoidal groupoids, including the case of monoids with operators. This cohomology is also compared to the classical Eilenberg-Mac Lane and Hochschild-Mitchell cohomologies. Connections are also established with the Lausch-Loganathan cohomology theory for inverse semigroups, the Gabriel-Zisman cohomology of simplicial sets, the Wells cohomology of small categories (also known as Baues-Wirsching cohomology), Grothendieck sheaf cohomology, and finally Beck's triple cohomology. It also establishes connections with Grillet's cohomology theory for commutative semigroups. The monograph is aimed at researchers in the theory of monoids, or even semigroups, and its interface with category theory, homological algebra, and related fields. However, it is also written to be accessible to graduate students in mathematics and mathematicians in general.
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650 2 4 $a Geometry. $3 183883
650 2 4 $a Topology. $3 185965
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