03454nam a22005655i 4500 978-3-031-50258-3 DE-He213 20251030111718.0 cr nn 008mamaa 240313s2024 sz | s |||| 0|eng d 9783031502583 978-3-031-50258-3 10.1007/978-3-031-50258-3 doi QA150-272 PBF bicssc MAT002000 bisacsh PBF thema Cegarra, Antonio M. author. aut http://id.loc.gov/vocabulary/relators/aut 72915 The Cohomology of Monoids [electronic resource] / by Antonio M. Cegarra, Jonathan Leech. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIV, 214 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda RSME Springer Series, 2509-8896 ; 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. Algebra. 1501 Algebraic topology. 72916 Geometry. 68763 Topology. 72917 Algebra. 1501 Algebraic Topology. 72918 Geometry. 68763 Topology. 72917 Leech, Jonathan. author. aut http://id.loc.gov/vocabulary/relators/aut 72919 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031502576 Printed edition: 9783031502590 Printed edition: 9783031502606 RSME Springer Series, 2509-8896 ; 12 72920 https://doi.org/10.1007/978-3-031-50258-3 ZDB-2-SMA ZDB-2-SXMS 58284 58284