Theorems · Theorem · category theory
CategoryTheory.Subobject.inf_isPullback
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Limits.HasPullbacks C] {A : C}
(f g : CategoryTheory.Subobject A), CategoryTheory.IsPullback ((f ⊓ g).ofLE f ⋯) ((f ⊓ g).ofLE g ⋯) f.arrow g.arrow- Defined in
- Mathlib.CategoryTheory.Subobject.Lattice
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Limits.Cone.ptproof · cited by 1,298
- CategoryTheory.Limits.HasPullbacksstatement and proof · cited by 439
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.IsPullbackstatement · cited by 320
- CategoryTheory.Subobject.underlyingstatement and proof · cited by 211
- CategoryTheory.Subobject.arrowstatement and proof · cited by 175
- CategoryTheory.Limits.PullbackConeproof · cited by 136
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Regular.frobeniusMorphism_isPullbackproof · cited by 0