Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.pullback_fst
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {P : CategoryTheory.MorphismProperty C} {X Y S : C} (f : X ⟶ S)
(g : Y ⟶ S) [inst_1 : CategoryTheory.Limits.HasPullback f g] [P.IsStableUnderBaseChangeAlong f],
P g → P (CategoryTheory.Limits.pullback.fst f g)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Limits.pullbackstatement · cited by 864
- CategoryTheory.Limits.pullback.fststatement · cited by 639
- CategoryTheory.Limits.HasPullbackstatement and proof · cited by 434
- CategoryTheory.IsPullback.of_hasPullbackproof · cited by 70
- CategoryTheory.IsPullback.flipproof · cited by 61
- CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlongstatement and proof · cited by 24
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsZariskiLocalAtTarget.descendsAlong_inf_quasiCompactproof · cited by 2
- CategoryTheory.MorphismProperty.eq_of_isomorphisms_descendsAlongproof · cited by 1
- CategoryTheory.MorphismProperty.hasOfPostcompProperty_iff_le_diagonalproof · cited by 0
- AlgebraicGeometry.IsStableUnderBaseChange.of_pullback_fst_of_isAffineproof · cited by 0