All Questions
Tagged with crossed-modules simplicial-stuff
4 questions
13
votes
2
answers
929
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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 \...
7
votes
0
answers
178
views
Stabilisation of crossed modules?
D. Conduché has introduced a notion of a stable crossed module ("Modules croisés généralisés de longueur 2", JPAA 34 (1984) pp155–178, doi:10.1016/0022-4049(84)90034-3, Def. 3.1).
Is there a ...
3
votes
0
answers
189
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Geometric realization of crossed square
Given a crossed square of groups, you can "totalize" it and get a 2 crossed module in the sense of Conduché "Modules croisés généralisés de longueur 2", then you can apply his ...
3
votes
0
answers
94
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Explicit examples of 4-cocycles over finite 2-groups
By a (finite) 2-group $X$, I mean a finite group $G$, a finite abelian group $A$, an action of $G$ on $\operatorname{Aut}(A)$, as well as a 3-cocycle $\alpha\in H^3(BG, A)$. They are also equivalent ...