CatDat

Implication Details

Assumptions: left exact

Conclusions: preserves equalizers, preserves finite products, preserves monomorphisms

Proof: Finite products and equalizers are special cases of finite limits. Moreover, a morphism $f : X \to Y$ is a monomorphism if and only the square $$\begin{CD} X @>{\id_X}>> X \\ @V{\id_X}VV @VV{f}V \\ X @>>{f}> Y \end{CD}$$ is a pullback square, and pullbacks are special cases of finite limits.