Groupoid cores as animae

Example 1.1.5. Every 1-category \(C\) gives rise to an anima \(C^{\simeq }\), called its groupoid core. The elements of \(C^{\simeq }\) are the objects of \(C\). The anima \(C^{\simeq }(X,Y)\) between two objects \(X\) and \(Y\) is the set of isomorphisms between \(X\) and \(Y\) (regarded as an anima via the previous example).