Theorems · Definition · category theory

CategoryTheory.monadicCreatesColimitsOfPreservesColimits

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (R : CategoryTheory.Functor D C) →
          [CategoryTheory.MonadicRightAdjoint R] →
            [CategoryTheory.Limits.PreservesColimitsOfSize.{v, u, v₂, v₁, u₂, u₁} R] →
              CategoryTheory.CreatesColimitsOfSize.{v, u, v₂, v₁, u₂, u₁} R

A monadic functor creates colimits if it preserves colimits.

Defined in

Mathlib.CategoryTheory.Monad.Limits

Cited by

0 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonadicRightAdjointCategoryTheory.Limits.PreservesColimitsOfSize