(also nonabelian homological algebra)
Context
Basic definitions
Stable homotopy theory notions
Constructions
Lemmas
Homology theories
Theorems
The Moore complex of a simplicial group (or, more generally, any simplicially enriched groupoid), carries a lot more structure that just a chain complex of group(oid)s. This structure is its structure as a hypercrossed complex. The notion was introduced by Pilar Carrasco in her thesis.
3-group, 2-crossed module / crossed square, differential 2-crossed module
∞-group, simplicial group, crossed complex, hypercrossed complex
Pilar Carrasco, 1987, Complejos Hipercruzados, Cohomologia y Extensiones, Ph.D. thesis, Universidad de Granada.
P. Carrasco and A. M. Cegarra, Group-theoretic Algebraic Models for Homotopy Types, J. Pure Appl. Alg., 75, (1991), 195 – 235. https://doi.org/10.1016/0022-4049(91)90133-M
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