UID:
almahu_9949709279002882
Umfang:
XIV, 214 p.
,
online resource.
Ausgabe:
1st ed. 2024.
ISBN:
9783031502583
Serie:
RSME Springer Series, 12
Inhalt:
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.
In:
Springer Nature eBook
Weitere Ausg.:
Printed edition: ISBN 9783031502576
Weitere Ausg.:
Printed edition: ISBN 9783031502590
Weitere Ausg.:
Printed edition: ISBN 9783031502606
Sprache:
Englisch
DOI:
10.1007/978-3-031-50258-3
URL:
https://doi.org/10.1007/978-3-031-50258-3
URL:
Volltext
(URL des Erstveröffentlichers)
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