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Record Nr. |
UNINA9910616380303321 |
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Autore |
Grillet Pierre A (Pierre Antoine), <1941-> |
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Titolo |
The cohomology of commutative semigroups : an overview / / Pierre Antoine Grillet |
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Pubbl/distr/stampa |
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Cham, Switzerland : , : Springer, , [2022] |
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©2022 |
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ISBN |
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9783031082122 |
9783031082115 |
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Descrizione fisica |
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1 online resource (191 pages) |
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Collana |
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Lecture Notes in Mathematics ; ; v.2307 |
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Disciplina |
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Soggetti |
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Cohomology operations |
Commutative semigroups |
Homologia |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Intro -- Preface -- Contents -- List of Symbols -- 1 The Beginning -- 1.1 The Congruence H -- 1.1.1 Basics -- 1.1.2 Commutative Group Coextensions -- 1.2 Construction -- 1.2.1 Schreier's Method -- 1.2.2 Split Coextensions -- 1.2.3 Enter Cohomology -- 1.2.4 Finite Semigroups -- 2 Beck Cohomology -- 2.1 General Beck Cohomology -- 2.1.1 Simple Cohomology -- 2.1.2 Abelian Group Objects -- 2.1.3 Objects Over S -- 2.1.4 Beck Cohomology -- 2.1.5 Main Properties -- 2.1.6 Beck Extensions -- 2.2 Commutative Semigroups -- 2.2.1 Commutative Semigroups Over S -- 2.2.2 Abelian Group Objects Over S -- 2.2.3 Beck Extensions of S -- 2.3 Beck Cohomology of Commutative Semigroups -- 2.3.1 The `Free Commutative Semigroup' Adjunction -- 2.3.2 The `Free Commutative Semigroup' Comonad -- 2.3.3 Cochains -- 2.3.4 Cohomology -- 2.3.5 Properties -- 3 Symmetric Cohomology -- 3.1 Definition -- 3.1.1 Cochains -- 3.1.2 Symmetric Cochains -- 3.1.3 Symmetric Cohomology -- 3.1.4 An Example -- 3.2 Comparison with Beck Cohomology -- 3.2.1 Dimension 1 -- 3.2.2 Dimension 2 -- 3.2.3 Dimensions 3 and 4 -- 3.3 Main Properties -- 3.4 Normalization -- 3.4.1 Dimension 2 -- 3.4.2 Dimension 3 -- 4 Calvo-Cegarra |
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