Theorems · Theorem · category theory
CategoryTheory.Subobject.factors_comp_arrow
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} {P : CategoryTheory.Subobject Y}
(f : X ⟶ CategoryTheory.Subobject.underlying.obj P), P.Factors (CategoryTheory.CategoryStruct.comp f P.arrow)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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 and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.underlyingstatement and proof · cited by 211
- CategoryTheory.Subobject.arrowstatement and proof · cited by 175
- CategoryTheory.Subobject.Factorsstatement · cited by 56
- CategoryTheory.Subobject.factors_iffproof · cited by 12
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.finset_inf_arrow_factorsproof · cited by 2
- CategoryTheory.Subobject.inf_isPullbackproof · cited by 1