# nLab hypercrossed complex

### Context

#### Homological algebra

homological algebra

and

nonabelian homological algebra

diagram chasing

### Theorems

#### Higher category theory

higher category theory

# 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.