Let $\mathcal{C}$ be an abelian category, $\mathcal{Ab}$ the category of abelian groups and $Lex(\mathcal{C}, \mathcal{B})$ the category of left exact functors between abelian categories.

**What is the simplest way (or at least a way) to prove that $Lex(\mathcal{A},\mathcal{Ab})$ is cocomplete and has an injective Cogenerator?**