[David Tanzer wrote](https://forum.azimuthproject.org/discussion/comment/16164/#Comment_16164)

> Reflexivity follows from the existence of identity morphisms in a category. Transitivity follows from the fact that given morphisms \\(f: A \to B\\), and \\(g: B \to C\\), the composite morphism taking \\(A \to C\\) is provided by the category.

Right! So reflexivity in a preorder is secretly the identity morphisms in a specially simple sort of category, while transitivity is really just composition! This is one of those nice little "aha!" moments where category theory starts unifying concepts and eliminating redundancy, freeing up neurons for deeper thoughts.

> Reflexivity follows from the existence of identity morphisms in a category. Transitivity follows from the fact that given morphisms \\(f: A \to B\\), and \\(g: B \to C\\), the composite morphism taking \\(A \to C\\) is provided by the category.

Right! So reflexivity in a preorder is secretly the identity morphisms in a specially simple sort of category, while transitivity is really just composition! This is one of those nice little "aha!" moments where category theory starts unifying concepts and eliminating redundancy, freeing up neurons for deeper thoughts.