Theorems · Inductive type · category theory

CategoryTheory.Limits.PreservesColimitsOfShape

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

We say that F preserves colimits of shape J if F preserves colimits for every diagram K : J ⥤ C, i.e., F maps colimit cocones over K to colimit cocones.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Basic

Cited by

222 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category