Do they form a category? Let me be more specific:
Let $\mathcal{C}$ be a category andd denote by $I(\mathcal{C})$ the collection of injective objects in $\mathcal{C}$ (with respect to monomorphisms). Can we make $I(\mathcal{C})$ into a category? What are the morphisms? And is this (potential) category studied somewhere in the literature?