Theorems · Definition · category theory
Types.monoOverEquivalenceSet
(α : Type u) → CategoryTheory.MonoOver α ≌ Set α
The category of MonoOver α, for α : Type u, is equivalent to the partial order Set α.
- Defined in
- Mathlib.CategoryTheory.Subobject.Types
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Quiver.Homproof · cited by 32,603
- Set.rangeproof · cited by 4,705
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- CategoryTheory.ObjectProperty.FullSubcategory.objproof · cited by 1,316
- CategoryTheory.Overstatement · cited by 935
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.homOfLEproof · cited by 554
- CategoryTheory.Over.leftproof · cited by 541
- TypeCat.ofHomproof · cited by 389
- CategoryTheory.Over.homproof · cited by 370
Cited by7
Results whose statement or proof uses this declaration.
- Types.monoOverEquivalenceSet_counitIsostatement and proof · cited by 0
- Types.monoOverEquivalenceSet_functor_mapstatement and proof · cited by 0
- Types.monoOverEquivalenceSet_functor_objstatement and proof · cited by 0
- Types.monoOverEquivalenceSet_inverse_mapstatement and proof · cited by 0
- Types.monoOverEquivalenceSet_inverse_objstatement and proof · cited by 0
- Types.monoOverEquivalenceSet_unitIsostatement and proof · cited by 0
- Types.subobjectEquivSetproof · cited by 0