Theorems · Theorem · category theory

CategoryTheory.Limits.pullback.diagonal_fst_assoc

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {X Y : C} (f : X ⟶ Y)
  [inst_1 : CategoryTheory.Limits.HasPullback f f] {Z : C} (h : X ⟶ Z),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.diagonal f)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.pullback.fst f f) h) =
    h

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Diagonal
Cited by: 3 results in Mathlib
Foundations: Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasPullback

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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.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.Category.id_compproof · cited by 1,998
CategoryTheory.Limits.pullback.fststatement and proof · cited by 639
CategoryTheory.Limits.HasPullbackstatement and proof · cited by 434
CategoryTheory.Limits.pullback.diagonalObjstatement · cited by 80
CategoryTheory.Limits.pullback.diagonalstatement and proof · cited by 67
CategoryTheory.Limits.pullback.diagonal_fstproof · cited by 21

Cited by3

Results whose statement or proof uses this declaration.

AlgebraicGeometry.Scheme.Pullback.range_diagonal_subset_diagonalCoverDiagonalRangeproof · cited by 1
CategoryTheory.Limits.pullback.comp_diagonalproof · cited by 1
AlgebraicGeometry.IsSeparated.of_valuativeCriterionproof · cited by 1