Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.isLeftAdjoint_pushout
∀ {T : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} T] (P : CategoryTheory.MorphismProperty T) {X Y : T}
[P.IsStableUnderComposition] (f : X ⟶ Y) [inst_2 : P.HasPushoutsAlong f]
[inst_3 : P.IsStableUnderCobaseChangeAlong f],
P f → (CategoryTheory.MorphismProperty.Under.pushout P ⊤ f).IsLeftAdjoint- Cited by
- 0 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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
- Top.topstatement and proof · cited by 9,680
- CategoryTheory.Functor.idstatement · cited by 3,333
- CategoryTheory.Discretestatement · cited by 2,447
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Functor.fromPUnitstatement · cited by 769
- CategoryTheory.MorphismProperty.IsStableUnderCompositionstatement and proof · cited by 84
- CategoryTheory.MorphismProperty.Understatement · cited by 43
- CategoryTheory.Functor.IsLeftAdjointstatement · cited by 28
- CategoryTheory.MorphismProperty.IsStableUnderCobaseChangeAlongstatement and proof · cited by 16
- CategoryTheory.MorphismProperty.Under.pushoutstatement · cited by 15
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