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020 _a9783031502583
_9978-3-031-50258-3
024 7 _a10.1007/978-3-031-50258-3
_2doi
050 4 _aQA150-272
072 7 _aPBF
_2bicssc
072 7 _aMAT002000
_2bisacsh
072 7 _aPBF
_2thema
100 1 _aCegarra, Antonio M.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_972915
245 1 4 _aThe Cohomology of Monoids
_h[electronic resource] /
_cby Antonio M. Cegarra, Jonathan Leech.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXIV, 214 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aRSME Springer Series,
_x2509-8896 ;
_v12
520 _aThis 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 _aAlgebra.
_91501
650 0 _aAlgebraic topology.
_972916
650 0 _aGeometry.
_968763
650 0 _aTopology.
_972917
650 1 4 _aAlgebra.
_91501
650 2 4 _aAlgebraic Topology.
_972918
650 2 4 _aGeometry.
_968763
650 2 4 _aTopology.
_972917
700 1 _aLeech, Jonathan.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_972919
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031502576
776 0 8 _iPrinted edition:
_z9783031502590
776 0 8 _iPrinted edition:
_z9783031502606
830 0 _aRSME Springer Series,
_x2509-8896 ;
_v12
_972920
856 4 0 _uhttps://doi.org/10.1007/978-3-031-50258-3
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c58284
_d58284