Left lifting property against monomorphisms
= Left lifting property against monomorphisms
A map $e:X\to Y$ has this property if every commutative square with $e$ as its left side and a <monomorphism> $m:A\to B$ as its right side has a diagonal filler $t:Y\to A$. The filler is unique because $m$ is monic. This definition does not itself stipulate that $e$ is an <epimorphism>; binary products imply that conclusion by testing against the <categorical diagonal>.