Theorems · Theorem · category theory
CategoryTheory.Bicategory.isRightAdjoint_TFAE
∀ {B : Type u} [inst : CategoryTheory.Bicategory B] {a b : B} (u : b ⟶ a),
[CategoryTheory.Bicategory.IsRightAdjoint u,
CategoryTheory.Bicategory.HasAbsLeftKanLift u (CategoryTheory.CategoryStruct.id a),
∃ (x : CategoryTheory.Bicategory.HasLeftKanLift u (CategoryTheory.CategoryStruct.id a)),
CategoryTheory.Bicategory.LanLift.CommuteWith u (CategoryTheory.CategoryStruct.id a) u].TFAE- Cited by
- 0 results in Mathlib
- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Bicategory
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Cites16
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.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.Bicategorystatement and proof · cited by 1,587
- List.TFAEstatement · cited by 102
- List.tfae_of_cycleproof · cited by 83
- CategoryTheory.Bicategory.HasLeftKanLiftstatement and proof · cited by 19
- CategoryTheory.Bicategory.LanLift.CommuteWithstatement and proof · cited by 10
- CategoryTheory.Bicategory.lanLiftIsKanproof · cited by 6
- CategoryTheory.Bicategory.LanLift.CommuteWith.isKanproof · cited by 4
- CategoryTheory.Bicategory.HasAbsLeftKanLiftstatement and proof · cited by 3
- CategoryTheory.Bicategory.IsRightAdjointstatement and proof · cited by 3
- CategoryTheory.Bicategory.IsRightAdjoint.mkproof · cited by 1
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