The crossed-modules tag has no usage guidance.

**12**

votes

**2**answers

402 views

### Group cohomology without G-modules (a.k.a. what does this bar construction compute?)

Without any prior exposure to the cohomology of groups, one might naively proceed by replacing a group by a sort of resolution.
For instance, let's take $G = \mathbb{Z}^2$, and "resolve":
$$ 0 \to ...

**3**

votes

**1**answer

346 views

### Maps between classifying spaces

Let $G$ be a discrete group and let $BG \simeq K(G,1)$ be its classifying space. Let $H$ be a topological group with classifying space $BH$.
In case $H$ is also discrete, it was pointed out in the ...

**1**

vote

**0**answers

65 views

### Crossed modules quasi-isomorphic to a quasi-abelian crossed module

This is a follow-up of this question,
where the definition of a quasi-abelian crossed module was given.
Namely, a crossed module $\partial\colon F\to G$ is quasi-abelian
if the embedding ...

**3**

votes

**1**answer

160 views

### Non-quasi-abelian braided crossed modules

A right crossed module is a homomorphism of groups
$\partial\colon F\to G$
together with a right action of $G$ on $F$, written
$(g,f)\mapsto f^g$,
satisfying certain conditions.
The question is, ...