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:
“The best way to teach a child restraint and generosity is to be a model of those qualities yourself. If your child sees that you want a particular item but refrain from buying it, either because it isn’t practical or because you can’t afford it, he will begin to understand restraint. Likewise, if you donate books or clothing to charity, take him with you to distribute the items to teach him about generosity.”
—Lawrence Balter (20th century)
“All cultural change reduces itself to a difference of categories. All revolutions, whether in the sciences or world history, occur merely because spirit has changed its categories in order to understand and examine what belongs to it, in order to possess and grasp itself in a truer, deeper, more intimate and unified manner.”
—Georg Wilhelm Friedrich Hegel (1770–1831)