Right-factor cancellation for lifting-only strong morphisms
= Right-factor cancellation for lifting-only strong morphisms
If $gf$ has the <left lifting property against monomorphisms>, so does $g$. Precompose a lifting square for $g$ with $f$ and lift the composite. To check the remaining triangle, cancel the monic side of the square, rather than cancelling $f$. In particular, a monic right factor of a lifting-only strong morphism is an <isomorphism>.