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:
“We crossed a deep and wide bay which makes eastward north of Kineo, leaving an island on our left, and keeping to the eastern side of the lake. This way or that led to some Tomhegan or Socatarian stream, up which the Indian had hunted, and whither I longed to go. The last name, however, had a bogus sound, too much like sectarian for me, as if a missionary had tampered with it; but I knew that the Indians were very liberal. I think I should have inclined to the Tomhegan first.”
—Henry David Thoreau (18171862)