Theorems · Theorem · algebraic geometry
CategoryTheory.MorphismProperty.Over.pullback.congr_simp
∀ {T : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} T] (P Q : CategoryTheory.MorphismProperty T)
[inst_1 : Q.IsMultiplicative] {X Y : T} (f f_1 : X ⟶ Y) (e_f : f = f_1) [inst_2 : P.HasPullbacksAlong f]
[inst_3 : P.IsStableUnderBaseChangeAlong f] [inst_4 : Q.IsStableUnderBaseChange],
CategoryTheory.MorphismProperty.Over.pullback P Q f = CategoryTheory.MorphismProperty.Over.pullback P Q f_1- Defined in
- Mathlib.AlgebraicGeometry.ColimitsOver
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- CategoryTheory.Functorstatement · cited by 16,252
- Top.topstatement · 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.IsMultiplicativestatement and proof · cited by 332
- CategoryTheory.MorphismProperty.IsStableUnderBaseChangestatement and proof · cited by 131
- CategoryTheory.MorphismProperty.Overstatement · cited by 94
- CategoryTheory.MorphismProperty.Over.pullbackstatement and proof · cited by 42
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