Theorems · Theorem · category theory
CategoryTheory.Limits.reflectsLimitsOfShape_of_reflectsIsomorphisms
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
{J : Type w} [inst_2 : CategoryTheory.Category.{w', w} J] {G : CategoryTheory.Functor C D} [G.ReflectsIsomorphisms]
[CategoryTheory.Limits.HasLimitsOfShape J C] [CategoryTheory.Limits.PreservesLimitsOfShape J G],
CategoryTheory.Limits.ReflectsLimitsOfShape J GIf C has limits of shape J and G preserves them, then if G reflects isomorphisms then it
reflects limits of shape J.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Functorstatement and proof · cited by 16,252
- CategoryTheory.Limits.HasLimitsOfShapestatement and proof · cited by 223
- CategoryTheory.Limits.PreservesLimitsOfShapestatement and proof · cited by 156
- CategoryTheory.Functor.ReflectsIsomorphismsstatement and proof · cited by 82
- CategoryTheory.Limits.ReflectsLimitsOfShapestatement · cited by 30
- CategoryTheory.Limits.reflectsLimit_of_reflectsIsomorphismsproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.reflectsLimits_of_reflectsIsomorphismsproof · cited by 1
- CategoryTheory.adhesive_of_preserves_and_reflects_isomorphismproof · cited by 0
- CategoryTheory.finitaryExtensive_of_preserves_and_reflects_isomorphismproof · cited by 0