Category Theory in Coq

The core theory avoids axioms, ensuring constructive proofs and higher reliability for formal verification, as stated in the design decisions.

Leverages opposite categories to define dual concepts like comonads in one line, reducing code duplication and proof effort through built-in duality simplifications.

Includes a sub-library for applied category theory in Coq, mimicking Haskell's monad hierarchy while using general categorical proofs to establish lawfulness, as shown in the programming sub-library examples.

Uses homsetoids (crelations) instead of strict equality, allowing customizable notions of arrow equivalence for different categories, though it increases proof obligations.

Provides extensive notations for morphisms, functors, and categorical operations, improving readability and expressiveness for users familiar with category theory texts.