nLab
hypercrossed complex

Context

Homological algebra

homological algebra

and

nonabelian homological algebra

Context

Basic definitions

Stable homotopy theory notions

Constructions

Lemmas

diagram chasing

Homology theories

Theorems

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

Contents

Idea

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.

References

  • 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.

Revised on September 14, 2011 15:44:41 by Urs Schreiber (131.211.239.174)