Example 1.1.9. Every anima \(X\) defines an \(\infty \)-category, again denoted \(X\), whose objects are the elements of \(X\) and whose animae of morphisms from \(x\) to \(y\) are the animae \(X(x,y)\) of equalities. The categorical composition corresponds to the fact that equality is reflexive and transitive. Symmetry of equality is encoded by the condition that every morphism in \(X\) admits an inverse.
In fact, in our axiomatic setup, this is how animae will be defined: as those \(\infty \)-categories in which every morphism is invertible. The animae \(X(x,y)\) from before are then nothing but the hom animae \(\Hom _X(x,y)\) of this \(\infty \)-category.
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