Theorems · Inductive type · category theory

CategoryTheory.Limits.PreservesColimit

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {J : Type w} →
          [inst_2 : CategoryTheory.Category.{w', w} J] → CategoryTheory.Functor J C → CategoryTheory.Functor C D → Prop

A functor F preserves colimits of K (written as PreservesColimit K F) if F maps any colimit cocone over K to a colimit cocone.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Basic

Cited by

278 results in Mathlib

Foundations

Depth 2 from the axioms, rests on 3 definitions · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category