Theorems · Theorem · category theory
CategoryTheory.Subobject.underlyingIso_arrow
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} (f : X ⟶ Y) [inst_1 : CategoryTheory.Mono f],
CategoryTheory.CategoryStruct.comp (CategoryTheory.Subobject.underlyingIso f).inv
(CategoryTheory.Subobject.mk f).arrow =
f- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.mapproof · cited by 8,698
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.Subobject.underlyingstatement · cited by 211
- CategoryTheory.Subobject.arrowstatement · cited by 175
- CategoryTheory.Subobject.mkstatement · cited by 109
- CategoryTheory.Over.wproof · cited by 42
Cited by22
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mkproof · cited by 15
- CategoryTheory.Limits.kernelSubobject_arrow'proof · cited by 9
- CategoryTheory.Subobject.ofMkLEMk_compproof · cited by 7
- CategoryTheory.Limits.imageSubobject_arrow'proof · cited by 7
- CategoryTheory.Subobject.eq_mk_of_commproof · cited by 2
- CategoryTheory.Subobject.le_mk_of_commproof · cited by 1
- CategoryTheory.Subobject.pullback_objproof · cited by 1
- CategoryTheory.Limits.imageSubobject_le_mkproof · cited by 1
- CategoryTheory.Limits.equalizerSubobject_arrow'proof · cited by 1
- CategoryTheory.Subobject.isPullback_auxproof · cited by 1
- CategoryTheory.Subobject.underlyingIso_inv_top_arrowproof · cited by 1