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:
“AIDS occupies such a large part in our awareness because of what it has been taken to represent. It seems the very model of all the catastrophes privileged populations feel await them.”
—Susan Sontag (b. 1933)
“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)