Documentation for natural transformations

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Frederik Hanghøj Iversen 2018-02-23 17:37:27 +01:00
parent 689a6467c6
commit dd11b69c71

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@ -1,3 +1,22 @@
-- This module Essentially just provides the data for natural transformations
--
-- This includes:
--
-- The types:
--
-- * Transformation - a family of functors
-- * Natural - naturality condition for transformations
-- * NaturalTransformation - both of the above
--
-- Elements of the above:
--
-- * identityTrans - the identity transformation
-- * identityNatural - naturality for the above
-- * identity - both of the above
--
-- Functions for manipulating the above:
--
-- * A composition operator.
{-# OPTIONS --allow-unsolved-metas --cubical #-} {-# OPTIONS --allow-unsolved-metas --cubical #-}
module Cat.Category.NaturalTransformation where module Cat.Category.NaturalTransformation where
open import Agda.Primitive open import Agda.Primitive
@ -29,6 +48,8 @@ module NaturalTransformation {c c' d d' : Level}
NaturalTransformation : Set (c c' d') NaturalTransformation : Set (c c' d')
NaturalTransformation = Σ Transformation Natural NaturalTransformation = Σ Transformation Natural
-- TODO: Since naturality is a mere proposition this principle can be
-- simplified.
NaturalTransformation≡ : {α β : NaturalTransformation} NaturalTransformation≡ : {α β : NaturalTransformation}
(eq₁ : α .proj₁ β .proj₁) (eq₁ : α .proj₁ β .proj₁)
(eq₂ : PathP (eq₂ : PathP