Mathlib Map

Theorems · Definition · category theory

CategoryTheory.ChosenPullbacksAlong.cartesianMonoidalCategoryOver

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [CategoryTheory.ChosenPullbacks C] → (X : C) → CategoryTheory.CartesianMonoidalCategory (CategoryTheory.Over X)

A computable instance of CartesianMonoidalCategory for Over X when C has chosen pullbacks. Contrast this with the noncomputable instance provided by CategoryTheory.Over.cartesianMonoidalCategory.

Defined in
Mathlib.CategoryTheory.LocallyCartesianClosed.Over
Cited by
49 results in Mathlib
Foundations
Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.ChosenPullbacks
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.toOverIteratedSliceForwardIsoPullback · cited by 2CategoryTheory.toOverIter…CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_fst · cited by 1Over.associator_hom_left_…CategoryTheory.ChosenPullbacksAlong.Over.associator_hom_left_snd_snd · cited by 1Over.associator_hom_left_…CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_fst · cited by 1Over.associator_inv_left_…CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_fst_snd · cited by 1Over.associator_inv_left_…CategoryTheory.ChosenPullbacksAlong.Over.associator_inv_left_snd · cited by 1Over.associator_inv_left_…CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_fst · cited by 1Over.leftUnitor_inv_left_…CategoryTheory.ChosenPullbacksAlong.Over.leftUnitor_inv_left_snd · cited by 1Over.leftUnitor_inv_left_…CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_fst · cited by 1Over.rightUnitor_inv_left…CategoryTheory.ChosenPullbacksAlong.Over.rightUnitor_inv_left_snd · cited by 1Over.rightUnitor_inv_left…CategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_fst · cited by 1Over.tensorHom_left_fstCategoryTheory.ChosenPullbacksAlong.Over.tensorHom_left_snd · cited by 1Over.tensorHom_left_sndCategoryTheory.ChosenPullbacksAlong.Over.tensorObj_ext · cited by 1Over.tensorObj_extCategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_fst · cited by 1Over.whiskerLeft_left_fstCategoryTheory.ChosenPullbacksAlong.Over.whiskerLeft_left_snd · cited by 1Over.whiskerLeft_left_sndCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.CartesianMonoidalCategory · cited by 947CategoryTheory.CartesianM…CategoryTheory.Over · cited by 935CategoryTheory.OverCategoryTheory.Over.hom · cited by 370Over.homCategoryTheory.Over.mk · cited by 203Over.mkCategoryTheory.Over.homMk · cited by 115Over.homMkCategoryTheory.ChosenPullbacks · cited by 49CategoryTheory.ChosenPull…CategoryTheory.Limits.asEmptyCone · cited by 12Limits.asEmptyConeCategoryTheory.Limits.IsTerminal.ofUniqueHom · cited by 5IsTerminal.ofUniqueHomCategoryTheory.ChosenPullbacksAlong.binaryFan · cited by 0ChosenPullbacksAlong.bina…CategoryTheory.ChosenPullbacksAlong.binaryFanIsBinaryProduct · cited by 0ChosenPullbacksAlong.bina…CategoryTheory.CartesianMonoidalCategory.ofChosenFiniteProducts · cited by 0CartesianMonoidalCategory…ChosenPullbacksAlong.cartesia…CITED BYCITES

Cites13

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by50

Results whose statement or proof uses this declaration.