Slate - Morphisms

Definition 4.3. Let u ∈ ℕ, C be a/an u-small category, X, Y ∈ C. We define:

Hom(X, Y) := M_X,Y if C = [O(M_A,B)_{A,B ∈ O}(i_C)_C ∈ O(∘_D,E,F)_{D,E,F ∈ O}]_u (O is a set, M_A,B is a set for each A, B ∈ O, i_C ∈ M_C,C for each C ∈ O, ∘_D,E,F : M_E,F × M_D,E → M_D,F is an operation for each D, E, F ∈ O with suitable conditions)

We write “let F : X → Y be a morphism” for “let F ∈ Hom(X, Y).”

References.