Theorems · Theorem · category theory
CategoryTheory.Subobject.mk_le_of_comm
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {B A : C} {X : CategoryTheory.Subobject B} {f : A ⟶ B}
[inst_1 : CategoryTheory.Mono f] (g : A ⟶ CategoryTheory.Subobject.underlying.obj X),
CategoryTheory.CategoryStruct.comp g X.arrow = f → CategoryTheory.Subobject.mk f ≤ X- Defined in
- Mathlib.CategoryTheory.Subobject.Basic
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- 0 results in Mathlib
- Foundations
- Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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 and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.underlyingstatement and proof · cited by 211
- CategoryTheory.Subobject.arrowstatement and proof · cited by 175
- CategoryTheory.Subobject.mkstatement and proof · cited by 109
- CategoryTheory.Subobject.underlyingIsoproof · cited by 41
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