homotopy hypothesis-theorem
delooping hypothesis-theorem
stabilization hypothesis-theorem
(also nonabelian homological algebra)
Context
Basic definitions
Stable homotopy theory notions
Constructions
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Homology theories
Theorems
Crossed modules of groups, differential crossed modules (or Lie algebra crossed modules), and crossed modules of crossed modules, are a special case of an internal crossed module of objects in semi-abelian categories.
Crossed modules internal to semi-abelian categories, along with precrossed modules, were introduced in:
On further generalization to include crossed modules of monoids in even more general contexts than treated by semi-abelian categories:
Gabriella Böhm: Crossed modules of monoids I: relative categories, Appl. Categor. Struct. 27 (2019) 641-662 [doi:10.1007/s10485-019-09570-0]
Gabriella Böhm: Crossed modules of monoids II: Relative Crossed Modules, Appl Categor Struct 28 (2020) 601-653 [doi:10.1007/s10485-020-09592-z]
Gabriella Böhm: Crossed modules of monoids III: Simplicial monoids of Moore length 1, Appl. Categor. Struct. 29 (2021) 1-29 [doi:10.1007/s10485-020-09603-z]
On precrossed modules in Malcev categories:
Last revised on May 3, 2024 at 08:30:11. See the history of this page for a list of all contributions to it.