Notes on higher dimensional groups and related topics
نویسنده
چکیده
1 Crossed Modules and Cat1-Groups 4 1.1 Pre-crossed and Crossed Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Examples of Crossed Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 Properties of Crossed Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.4 Sub-crossed modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Properties of morphisms of crossed modules . . . . . . . . . . . . . . . . . . . . . . . . 7 1.6 Peiffer subgroup of a pre-crossed module . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.7 Free Crossed Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.8 The monoid version of free crossed modules . . . . . . . . . . . . . . . . . . . . . . . . 14 1.9 A Geometric Example of Crossed Modules . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.10 Semidirect Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.11 Cat1-groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.12 Pre-cat1-groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.13 Group Groupoids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.14 2-groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
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