There are quite a few formalisations of category theory for proof assistants. For a relatively recent overview, see: https://mathoverflow.net/questions/152497/

There are quite a few formalisations of category theory for proof assistants. For a relatively recent overview, see: https://mathoverflow.net/questions/152497/formalizations-of-category-theory-in-proof-assistants https://mathoverflow.net/questions/152497/formalizations-of-...