Theorems · Theorem · category theory
CategoryTheory.Subobject.mk_le_mk_of_comm
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {B A₁ A₂ : C} {f₁ : A₁ ⟶ B} {f₂ : A₂ ⟶ B}
[inst_1 : CategoryTheory.Mono f₁] [inst_2 : CategoryTheory.Mono f₂] (g : A₁ ⟶ A₂),
CategoryTheory.CategoryStruct.comp g f₂ = f₁ → CategoryTheory.Subobject.mk f₁ ≤ CategoryTheory.Subobject.mk f₂- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.Monostatement and proof · cited by 893
- CategoryTheory.Subobjectstatement · cited by 385
- CategoryTheory.Subobject.mkstatement · cited by 109
- CategoryTheory.MonoOver.homMkproof · cited by 18
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.Subobject.le_of_commproof · cited by 10
- CategoryTheory.Limits.imageSubobject_comp_leproof · cited by 3
- CategoryTheory.Subobject.mk_lt_mk_of_commproof · cited by 2
- CategoryTheory.Limits.imageSubobject_iso_compproof · cited by 2
- CategoryTheory.MonoOver.subobjectMk_le_mk_of_homproof · cited by 1
- CategoryTheory.IsGrothendieckAbelian.subobjectMk_of_isColimit_eq_iSupproof · cited by 1
- CategoryTheory.Subobject.ofLE_mk_le_mk_of_commstatement and proof · cited by 0