Theorems · Theorem · category theory
CategoryTheory.strongMono_of_strongMono
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {R Q P : C} (f : P ⟶ Q) (g : Q ⟶ R)
[CategoryTheory.StrongMono (CategoryTheory.CategoryStruct.comp f g)], CategoryTheory.StrongMono fIf f ≫ g is a strong monomorphism, then so is f.
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- Foundations
- Depth 11 from the axioms · uses propext, Classical.choice
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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.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Epiproof · cited by 688
- CategoryTheory.cancel_epiproof · cited by 380
- CategoryTheory.CommSqproof · cited by 158
- CategoryTheory.CommSq.liftproof · cited by 34
- CategoryTheory.CommSq.fac_leftproof · cited by 22
- CategoryTheory.Category.assoc'proof · cited by 19
- CategoryTheory.StrongMonostatement and proof · cited by 11
- CategoryTheory.mono_of_monoproof · cited by 9
- CategoryTheory.CommSq.mk'proof · cited by 4
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