A sparse category is a category with at most one morphism between each pair of objects.

Examples include posets, but many indexing categories (diagrams) for special shapes of (co)limits.

To construct a category instance one only needs to specify the category_struct part, as the axioms hold for free.

category_theory.sparse_category

Construct a category instance from a category_struct, using the fact that hom spaces are subsingletons to prove the axioms.