Mathlib Map

Theorems · Definition · category theory

CategoryTheory.CartesianMonoidalCategory.lift

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      {T X Y : C} → (T ⟶ X) → (T ⟶ Y) → (T ⟶ CategoryTheory.MonoidalCategoryStruct.tensorObj X Y)

Constructs a morphism to the product given its two components.

Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
Cited by
160 results in Mathlib
Foundations
Depth 26 from the axioms, rests on 151 definitions · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategory

Around this declaration

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

CategoryTheory.CartesianMonoidalCategory.prodComparison · cited by 41CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.lift_snd · cited by 37CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.lift_fst · cited by 36CartesianMonoidalCategory…SSet.ι₀ · cited by 18SSet.ι₀SSet.ι₁ · cited by 18SSet.ι₁CategoryTheory.CartesianMonoidalCategory.comp_lift · cited by 13CartesianMonoidalCategory…TopCat.ι₀ · cited by 11TopCat.ι₀TopCat.ι₁ · cited by 11TopCat.ι₁CategoryTheory.CartesianMonoidalCategory.lift_fst_snd · cited by 10CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.lift_whiskerLeft_assoc · cited by 9CartesianMonoidalCategory…CategoryTheory.ModObj.leftSMul · cited by 8ModObj.leftSMulCategoryTheory.CartesianMonoidalCategory.lift_whiskerRight_assoc · cited by 7CartesianMonoidalCategory…CategoryTheory.forgetAdjToOver · cited by 7CategoryTheory.forgetAdjT…CategoryTheory.CartesianMonoidalCategory.comp_lift_assoc · cited by 7CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_hom_assoc · cited by 6CartesianMonoidalCategory…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.CartesianMonoidalCategory · cited by 947CategoryTheory.CartesianM…CategoryTheory.CartesianMonoidalCategory.tensorProductIsBinaryProduct · cited by 6CartesianMonoidalCategory…CategoryTheory.Limits.BinaryFan.IsLimit.lift' · cited by 5IsLimit.lift'CartesianMonoidalCategory.liftCITED BYCITES

Cites6

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Cited by191

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