Theorems · Theorem · category theory
CategoryTheory.Subobject.underlying_arrow
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X : C} {Y Z : CategoryTheory.Subobject X} (f : Y ⟶ Z),
CategoryTheory.CategoryStruct.comp (CategoryTheory.Subobject.underlying.map f) Z.arrow = Y.arrow- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 3 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.
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.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.InducedCategory.Hom.homproof · cited by 850
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.underlyingstatement · cited by 211
- CategoryTheory.Subobject.arrowstatement · cited by 175
- CategoryTheory.Over.wproof · cited by 42
- CategoryTheory.Subobject.representativeproof · cited by 15
Cited by3
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.ofLE_arrowproof · cited by 23
- CategoryTheory.Subobject.underlying_arrow_assocproof · cited by 0
- CategoryTheory.Subobject.sSup_leproof · cited by 0