Crossed Module

In mathematics, and especially in homotopy theory, a crossed module consists of groups G and H, where G acts on H (which we will write on the left, ), and a homomorphism of groups

that is equivariant with respect to the conjugation action of G on itself:

and also satisfies the so-called Peiffer identity:

Read more about Crossed Module:  Origin, Examples, Classifying Space

Other articles related to "crossed module":

Crossed Module - Classifying Space
... Any crossed module has a classifying space BM with the property that its homotopy groups are Coker d, in dimension 1, Ker d in dimension 2, and 0 above 2 ...

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