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
Famous quotes containing the word crossed:
“One is not idle because one is absorbed. There is both visible and invisible labor. To contemplate is to toil, to think is to do. The crossed arms work, the clasped hands act. The eyes upturned to Heaven are an act of creation.”
—Victor Hugo (1802–1885)