Theorems · Theorem · order theory
NonemptyFinLinOrd.mono_iff_injective
∀ {A B : NonemptyFinLinOrd} (f : A ⟶ B),
CategoryTheory.Mono f ↔ Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom f)- Defined in
- Mathlib.Order.Category.NonemptyFinLinOrd
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- le_reflproof · cited by 2,061
- OrderHomstatement · cited by 934
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.InducedCategory.Hom.homproof · cited by 850
- CategoryTheory.cancel_monoproof · cited by 435
- OrderHom.extproof · cited by 55
- LinOrd.carrierstatement and proof · cited by 48
- NonemptyFinLinOrdstatement and proof · cited by 27
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