# Schreiber ana-inverse

Let $C$ be a category with weak equivalences and acyclic fibrations?, so that it admits a notion of ana-morphism?s.

An ana-inverse to a weak equivalence

$A \stackrel{\simeq}{\to} B$

is a span

$\array{ \hat B &\to^{f}& A \\ \downarrow^{\simeq_f} \\ B }$

such that

$\array{ & \hat B \\ & {}^f\swarrow \downarrow^{\simeq_f} \\ A &\stackrel{\simeq}{\to}& B } \,.$

We say a category with weak equivalences and acyclic fibrations? has ana-inverses if for every weak equivalence there exists such an ana-inverse.

Created on December 16, 2008 at 19:46:31. See the history of this page for a list of all contributions to it.