Abstract
We showed earlier that for the proarrow equipment ( ) ∗: TOP→TOPLEX co, the codomain is equivalent to codiscrete cofibrations in the domain (i.e. TOPLEX co∼CODCOFIB TOP). Here we show that M ∼CODCOFIB K for any proarrow equipment ( ) ∗: K → M satisfying a finitary exactness axiom. We give applications to topoi relative to a base and Grothendieck topoi.
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