Do Pushouts Preserve Monomorphisms?

The fact that monomorphisms are stable under pushouts in toposes plays a central role for Cisinski model structures such as notably the standard model structure on simplicial sets, where the monomorphisms are cofibrations and as such required to be closed under pushout (in particular).

Do functors preserve monomorphisms?

Monomorphisms are preserved by any right adjoint functor, or more generally any functors that preserves pullbacks. ... Any morphism from a terminal object is a monomorphism. The product of monomorphisms is a monomorphism.

Is monomorphism a limit?

Corollary: Being a monomorphism is a “limit property”: more precisely, any functor which preserves pullbacks (in particular any functor which preserves finite limits, in particular any functor which preserves all limits) preserves monomorphisms.