Theorems · Theorem · category theory

CategoryTheory.Functor.preservesColimitsOfShape_of_isZero

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  [CategoryTheory.Limits.HasZeroObject D] [CategoryTheory.Limits.HasZeroMorphisms D] (G : CategoryTheory.Functor C D),
  CategoryTheory.Limits.IsZero G →
    ∀ (J : Type u_1) [inst_4 : CategoryTheory.Category.{v_1, u_1} J], CategoryTheory.Limits.PreservesColimitsOfShape J G

A zero functor preserves colimits.

Defined in

Mathlib.CategoryTheory.Limits.Preserves.Shapes.Zero

Cited by

1 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Category