Theorems · Theorem · category theory
CategoryTheory.Subobject.pullback_map_self
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} [inst_1 : CategoryTheory.Limits.HasPullbacks C]
(f : X ⟶ Y) [inst_2 : CategoryTheory.Mono f] (g : CategoryTheory.Subobject X),
(CategoryTheory.Subobject.pullback f).obj ((CategoryTheory.Subobject.map f).obj g) = g- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement · cited by 19,642
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Limits.HasPullbacksstatement and proof · cited by 439
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Iso.appproof · cited by 253
- CategoryTheory.MonoOverproof · cited by 115
- CategoryTheory.Subobject.pullbackstatement · cited by 54
- CategoryTheory.Subobject.mapstatement · cited by 19
- CategoryTheory.MonoOver.pullbackMapSelfproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.inf_mapproof · cited by 0