Theorems · Theorem · category theory

CategoryTheory.Functor.preservesFiniteLimits_of_preservesHomology

∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Preadditive C]
  [inst_3 : CategoryTheory.Preadditive D] (F : CategoryTheory.Functor C D) [inst_4 : F.Additive] [F.PreservesHomology]
  [CategoryTheory.Limits.HasZeroObject C] [CategoryTheory.Limits.HasFiniteProducts C]
  [CategoryTheory.Limits.HasKernels C], CategoryTheory.Limits.PreservesFiniteLimits F

An additive functor which preserves homology preserves finite limits.

Defined in

Mathlib.Algebra.Homology.ShortComplex.ExactFunctor

Cited by

4 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.Functor.PreservesHomologyCategoryTheory.Limits.HasZeroObjectCategoryTheory.Limits.HasFiniteProductsCategoryTheory.Limits.HasKernels