Theorems · Theorem · category theory
CategoryTheory.Subobject.underlyingIso_hom_comp_eq_mk
∀ {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).hom f =
(CategoryTheory.Subobject.mk f).arrow- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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.Iso.homstatement · cited by 7,684
- 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.Subobject.underlyingIsostatement and proof · cited by 41
- CategoryTheory.Iso.eq_inv_compproof · cited by 34
Cited by15
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.mk_eq_mk_of_commproof · cited by 10
- CategoryTheory.Subobject.ofMkLEMk_compproof · cited by 7
- CategoryTheory.Limits.imageSubobject_arrowproof · cited by 6
- CategoryTheory.Limits.kernelSubobject_arrowproof · cited by 5
- CategoryTheory.Limits.equalizerSubobject_arrowproof · cited by 2
- CategoryTheory.CostructuredArrow.unop_left_comp_underlyingIso_hom_unopproof · cited by 1
- CategoryTheory.Subobject.ofLEMk_compproof · cited by 1
- CategoryTheory.Subobject.Classifier.χ_pullback_obj_mk_truth_arrowproof · cited by 1
- CategoryTheory.Subobject.ofLE_mk_le_mk_of_commproof · cited by 0
- CategoryTheory.Subobject.sSup_leproof · cited by 0
- CategoryTheory.Subobject.mk_le_of_commproof · cited by 0