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
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“For an artist to marry his model is as fatal as for a gourmet to marry his cook: the one gets no sittings, and the other gets no dinners.”
—Oscar Wilde (1854–1900)
“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)
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