Theorems · Definition · category theory

CategoryTheory.toOverUnitPullback

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      (X : C) →
        (CategoryTheory.toOverUnit C).comp
            (CategoryTheory.ChosenPullbacksAlong.pullback (CategoryTheory.SemiCartesianMonoidalCategory.toUnit X)) ≅
          CategoryTheory.toOver X

The isomorphism of functors toOverUnit C ⋙ ChosenPullbacksAlong.pullback (toUnit X) and toOver X.

Defined in: Mathlib.CategoryTheory.LocallyCartesianClosed.Over
Cited by: 2 results in Mathlib
Foundations: Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.CartesianMonoidalCategory

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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
CategoryTheory.Functor.objproof · cited by 19,642
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Functor.compstatement and proof · cited by 6,529
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement · cited by 1,384
CategoryTheory.CartesianMonoidalCategorystatement and proof · cited by 947
CategoryTheory.Overstatement · cited by 935
CategoryTheory.Iso.reflproof · cited by 727
CategoryTheory.NatIso.ofComponentsproof · cited by 178
CategoryTheory.SemiCartesianMonoidalCategory.toUnitstatement and proof · cited by 103
CategoryTheory.ChosenPullbacksAlong.pullbackstatement and proof · cited by 62

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.toOverUnitPullback_hom_app_leftstatement and proof · cited by 0
CategoryTheory.toOverUnitPullback_inv_app_leftstatement and proof · cited by 0