Theorems · Theorem · category theory

CategoryTheory.IsGrothendieckAbelian.of_equivalence

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  [inst_2 : CategoryTheory.Abelian C] [inst_3 : CategoryTheory.Abelian D]
  [CategoryTheory.IsGrothendieckAbelian.{w, v, u} C] (α : C ≌ D), CategoryTheory.IsGrothendieckAbelian.{w, v₂, u₂} D

Defined in: Mathlib.CategoryTheory.Abelian.GrothendieckCategory.Basic
Cited by: 1 results in Mathlib
Foundations: Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Category CategoryTheory.Abelian CategoryTheory.Abelian CategoryTheory.IsGrothendieckAbelian

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Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.Equivalence.inverseproof · cited by 1,130
CategoryTheory.Equivalencestatement and proof · cited by 601
CategoryTheory.IsFilteredproof · cited by 210
CategoryTheory.IsGrothendieckAbelianstatement and proof · cited by 30
CategoryTheory.Limits.HasFilteredColimitsOfSizeproof · cited by 13
CategoryTheory.locallySmall_of_faithfulproof · cited by 5
CategoryTheory.Adjunction.hasColimitsOfShape_of_equivalenceproof · cited by 4
CategoryTheory.HasSeparator.of_equivalenceproof · cited by 1
CategoryTheory.HasExactColimitsOfShape.of_codomain_equivalenceproof · cited by 1

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Sheaf.isGrothendieckAbelian_of_essentiallySmallproof · cited by 0