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The cohomology of monoids

Record Type:	Electronic resources : Monograph/item
Title/Author:	The cohomology of monoids/ by 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

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. 12..

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

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

778995
Cohomology operations.

LC Class. No.: QA169

Dewey Class. No.: 514.23

The cohomology of monoids
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100 1 $a Cegarra, Antonio M. $3 3716064
245 1 4 $a The cohomology of monoids $h [electronic resource] / $c by Antonio M. Cegarra, Jonathan Leech.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2024.
300 $a xiv, 214 p. : $b ill., digital ; $c 24 cm.
490 1 $a RSME Springer series, $x 2509-8896 ; $v v. 12
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.
650 0 $a Cohomology operations. $3 778995
650 0 $a Monoids. $3 897531
650 1 4 $a Algebra. $3 516203
650 2 4 $a Algebraic Topology. $3 891269
650 2 4 $a Geometry. $3 517251
650 2 4 $a Topology. $3 522026
700 1 $a Leech, Jonathan. $3 3716065
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a RSME Springer series ; $v v. 12. $3 3716066
856 4 0 $u https://doi.org/10.1007/978-3-031-50258-3
950 $a Mathematics and Statistics (SpringerNature-11649)