Initial and terminal animae

Example 1.7.10. The empty anima \(\emptyset \) is initial in \(\An \) and the one-point anima \(*\) is terminal in \(\An \). Indeed, by Axiom L below the hom anima \(\Hom _{\An }(X,Y)\) may be identified with the mapping anima \(\Map (X,Y) = \Fun (X,Y)^{\simeq }\), and both \(\Fun (\emptyset ,Y)\) and \(\Fun (X,*)\) are contractible.