[P]: Gee Brain, what d'you wanna do tonight?
[B]: Same thing we do every night, Pinky: try to formalise category theory!

Egads is a library where I define some category theory concepts and prove some elementary results. It's mainly for my own learning, but it might be somehow useful.

Category is the type of E-categories (categories where the objects form a type but the homs form setoids). This is possibly the final fling for E-categories before the cubical revolution. The Category definition is built up over many tiers with the intent of making definitions that read like “a monoid is a category with a single object”. These should be transparent (intensionally) to the users of Monoid. I have a couple of examples in Egads.Structure, and aim to add ring-like structures with the help of enriched categories.

This library depends on a few modules of stdlib. So far, this is:

• Data.Product
• Data.Product.Relation.Pointwise.NonDependent (including some definitions not yet in a release)
• Data.Unit
• Function
• Function.Equality
• Relation.Binary
• Relation.Binary.EqReasoning
• Relation.Binary.On
• Relation.Binary.PropositionalEquality
• Relation.Binary.SetoidReasoning

It wouldn't be too much work to replicate the definitions used here (yet, at least). The major incompatibility with stdlib is that I want to redo stdlib's algebra and order definitions to be categorial.