TITLE: Formalizations of category theory in proof assistants
QUESTION [40 upvotes]: What are the existing formalizations of category theory in proof assistants?

I'm primarily interested in public-domain code implementing category theory in a proof assistant (Coq, Agda, Isabelle/HOL, Mizar, NuPRL, Twelf, Lego, Idris, Matita, etc.), though I'm also interested in papers about formalizations of category theory in proof assistants.
I've added answers to this question for all of the papers and formalizations that I know about, and details about the constructions in my own repository as of the date of adding.  In addition to adding formalizations that you don't see on here, you should feel free to add details and improve the formatting of the other entries (especially including what language the formalization is in, what category theory it covers, links to papers presenting it and/or publicly available source code, whether or not it's under active development, what the newest version of the proof assistant it compiles with is, etc.).

REPLY [5 votes]: Wolfram Kahl's RATH-Agda formalisation :: http://relmics.mcmaster.ca/RATH-Agda/
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The basic category and allegory theory library of the RATH-Agda project, containing (only sporadically truly) literate theories ranging from semigroupoids, which are “categories without identities”, to “action lattice categories”, which are division allegories that are at the same time Kleene categories (i.e., typed Kleene algebras), including also monoidal categories.
These theories are intended as interfaces for high-level programming; this current collection includes implementations in particular using concrete relations, and a number of constructions, including quotients by (abstractions of) partial equivalence relations.
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