The Cohomology of Monoids (RSME Springer Series, 12)
Author: by Antonio M. Cegarra (Author), Jonathan Leech (Author)
Publisher: Springer
Edition: 2024th
Publication Date: 2024-03-14
Language: English
Print Length: 228 pages
ISBN-10: 3031502574
ISBN-13: 9783031502576
Book Description
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-Wirschingcohomology), 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.
From the Back Cover
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.
About the Author
Jonathan Leech earned his PhD from the University of California, Los Angeles, in 1969. He has imparted mathematical knowledge at various institutions, including the University of Tennessee, Missouri Western State University, and ultimately at Westmont College in Santa Barbara, California. He has held positions as a Visiting Professor at Case Western Reserve University, the Universidad de Granada in Spain, and Universidade Mackenzie in Brazil. Additionally, he has served as a scholar in residence at both the University of Sydney and the University of Tasmania in Australia, as well as the University of Ljubljana in Slovenia, the University of Petru Maior in Romania and several others. Throughout his academic career, Professor Leech has made many research contributions. In addition to his seminal contributions to the cohomology of monoids and semigroups, he has delved deeply into algebraic structures associated with semigroups. Indeed, he along with colleagues from around the world have established the fundamental principles of modern noncommutative lattice theory through various publications, including his book Noncommutative Lattices: Skew Lattices, Skew Boolean Algebras and Beyond in the Famnit Lectures series of the University of Primorska in Slovenia.
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