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Try doing some basic maths questions in the Lean Theorem Prover. Functions, real numbers, equivalence relations and groups. Click on README.md and then on "Open in CoCalc with one click".
Project: Xena
Views: 18536License: APACHE
/-
Copyright (c) 2019 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Scott Morrison
-/
import category_theory.functor_category
namespace category_theory
open category
universes v₁ u₁ -- declare the `v`'s first; see `category_theory.category` for an explanation
variables {C : Type u₁} [𝒞 : category.{v₁} C]
include 𝒞
class monad (T : C ⥤ C) :=
(η : 𝟭 _ ⟶ T)
(μ : T ⋙ T ⟶ T)
(assoc' : ∀ X : C, T.map (nat_trans.app μ X) ≫ μ.app _ = μ.app (T.obj X) ≫ μ.app _ . obviously)
(left_unit' : ∀ X : C, η.app (T.obj X) ≫ μ.app _ = 𝟙 _ . obviously)
(right_unit' : ∀ X : C, T.map (η.app X) ≫ μ.app _ = 𝟙 _ . obviously)
restate_axiom monad.assoc'
restate_axiom monad.left_unit'
restate_axiom monad.right_unit'
attribute [simp] monad.left_unit monad.right_unit
notation `η_` := monad.η
notation `μ_` := monad.μ
end category_theory