Theorems · Theorem · order theory
CategoryTheory.orderDualEquivalence_functor_map
∀ (X : Type u) [inst : Preorder X] {X_1 Y : Xᵒᵈ} (f : X_1 ⟶ Y),
(CategoryTheory.orderDualEquivalence X).functor.map f = (CategoryTheory.homOfLE ⋯).op- Defined in
- Mathlib.CategoryTheory.Category.Preorder
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement · cited by 8,081
- Preorderstatement and proof · cited by 7,952
- Quiver.Hom.opstatement · cited by 1,948
- CategoryTheory.Equivalence.functorstatement and proof · cited by 1,268
- OrderDualstatement and proof · cited by 927
- CategoryTheory.homOfLEstatement · cited by 554
- CategoryTheory.orderDualEquivalencestatement and proof · cited by 15
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