Generalization To Model Categories
In any model category, a weak equivalence between cofibrant-fibrant objects is a homotopy equivalence.
Read more about this topic: Whitehead Theorem
Famous quotes containing the words model and/or categories:
“When you model yourself on people, you should try to resemble their good sides.”
—Molière [Jean Baptiste Poquelin] (1622–1673)
“The analogy between the mind and a computer fails for many reasons. The brain is constructed by principles that assure diversity and degeneracy. Unlike a computer, it has no replicative memory. It is historical and value driven. It forms categories by internal criteria and by constraints acting at many scales, not by means of a syntactically constructed program. The world with which the brain interacts is not unequivocally made up of classical categories.”
—Gerald M. Edelman (b. 1928)