Page 7 - Textos de Matemática Vol. 45
P. 7
Contents
Introduction 1
1 Unital categories and intrinsic commutation 5
1.1 Notation............................... 5
1.2 Unitalcategories .......................... 5
1.3 C′-unitalcategories ........................ 8
1.4 Thefibrationofpoints.................
1.5 Mal’tsevcategories...................
2 Schreier and homogeneous split epimorphisms in monoids
...... 8 ...... 9
11
2.1 Definitionsandfirstproperties .................. 11
2.2 Examples of Schreier and homogeneous split epimorphisms . . 14
2.3 First properties of Schreier and homogeneous split epimorphisms 17
2.3.1 Stabilityproperties..................... 17
2.3.2 TheSchreiersplitshortfivelemma . . . . . . . . . . . . 22 2.4 The fibrations of Schreier and homogeneous points . . . . . . . 23
3 Schreier internal relations, categories and groupoids 29
3.1 Schreierreflexiverelationsandgraphs . . . . . . . . . . . . . . 30 3.2 Schreierinternalcategories .................... 35 3.3 Schreierinternalgroupoids .................... 38
4 Mal’tsev aspects of Mon related to Schreier split epimorphisms 43 4.1 Mal’tsevcategories......................... 43 4.2 Firstobservations.......................... 44 4.3 CentralityforSchreierrelations.................. 44 4.4 Doublecentralizingrelation .................... 47
5 Schreier and homogeneous representability 49
5.1 TheSchreiersplitextensionclassifier . . . . . . . . . . . . . . . 49 5.2 Semidirectproducts ........................ 52
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