Theorems · Theorem · category theory

CategoryTheory.Adjunction.leftAdjoint_preservesColimits

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F : CategoryTheory.Functor C D} {G : CategoryTheory.Functor D C} (adj : F ⊣ G),
  CategoryTheory.Limits.PreservesColimitsOfSize.{v, u, v₁, v₂, u₁, u₂} F

A left adjoint preserves colimits.

Defined in

Mathlib.CategoryTheory.Adjunction.Limits

Cited by

9 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category