Theorems · Inductive type · category theory

CategoryTheory.Limits.ReflectsColimit

{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 : C ⥤ D reflects colimits for K : J ⥤ C if whenever the image of a cocone over K under F is a colimit cocone in D, the cocone was already a colimit cocone in C. Note that we do not assume a priori that D actually has any colimits.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Basic

Cited by

33 results in Mathlib

Foundations

Depth 2 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category