Theorems · Theorem · category theory
CategoryTheory.Subobject.ofMkLEMk_comp
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {B A₁ A₂ : C} {f : A₁ ⟶ B} {g : A₂ ⟶ B}
[inst_1 : CategoryTheory.Mono f] [inst_2 : CategoryTheory.Mono g]
(h : CategoryTheory.Subobject.mk f ≤ CategoryTheory.Subobject.mk g),
CategoryTheory.CategoryStruct.comp (CategoryTheory.Subobject.ofMkLEMk f g h) g = f- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 7 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.
Cites15
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.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.Subobject.mkstatement and proof · cited by 109
- CategoryTheory.Subobject.underlyingIsoproof · cited by 41
- CategoryTheory.Subobject.ofLEproof · cited by 38
- CategoryTheory.Subobject.ofLE_arrowproof · cited by 23
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.isIso_iff_mk_eq_topproof · cited by 6
- CategoryTheory.Subobject.map_obj_injectiveproof · cited by 3
- CategoryTheory.Subobject.mk_lt_mk_of_commproof · cited by 2
- CategoryTheory.MonoOver.isIso_hom_left_iff_subobjectMk_eqproof · cited by 1
- CategoryTheory.IsGrothendieckAbelian.subobjectMk_of_isColimit_eq_iSupproof · cited by 1
- CategoryTheory.CostructuredArrow.unop_left_comp_ofMkLEMk_unopproof · cited by 0
- CategoryTheory.Subobject.ofMkLEMk_reflproof · cited by 0