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:
Other articles related to "crossed module":
... 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 ...
Famous quotes containing the word crossed:
“Twilight and evening bell.
And after that the dark!
And may there be no sadness of farewell,
When I embark;
For though from out our bourne of Time and Place
The flood may bear me far,
I hope to see my Pilot face to face
When I have crossed the bar.”
—Alfred Tennyson (18091892)