The Clowder Project

The core of $\mathcal{C}$ is the wide subcategory of $\mathcal{C}$ spanned by the isomorphisms of $\mathcal{C}$, i.e. the category $\mathsf{Core}\left(\mathcal{C}\right)$ where¹

1. 1. Objects. We have
   $$\text{Obj}\left(\mathsf{Core}\left(\mathcal{C}\right)\right)\stackrel{\text{def}}{=}\text{Obj}\left(\mathcal{C}\right).$$
2. 2. Morphisms. The morphisms of $\mathsf{Core}\left(\mathcal{C}\right)$ are the isomorphisms of $\mathcal{C}$.