Mathlib Map

Theorems · Definition · category theory

CategoryTheory.SemiCartesianMonoidalCategory.fst

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

The first projection from the product.

Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Basic
Cited by
184 results in Mathlib
Foundations
Depth 3 from the axioms, rests on 13 definitions · uses no axioms
Assumes
CategoryTheory.SemiCartesianMonoidalCategory

Around this declaration

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

CategoryTheory.CartesianMonoidalCategory.hom_ext · cited by 46CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.prodComparison · cited by 41CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.lift_fst · cited by 36CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.whiskerLeft_fst · cited by 24CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.comp_lift · cited by 13CartesianMonoidalCategory…CategoryTheory.SemiCartesianMonoidalCategory.fst_def · cited by 13SemiCartesianMonoidalCate…CategoryTheory.CartesianMonoidalCategory.whiskerRight_fst · cited by 13CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.tensorHom_fst · cited by 12CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.lift_fst_snd · cited by 10CartesianMonoidalCategory…SSet.Truncated.HomotopyCategory.BinaryProduct.functor · cited by 9BinaryProduct.functorCategoryTheory.GrpObj.commutator · cited by 9GrpObj.commutatorCategoryTheory.CartesianMonoidalCategory.associator_hom_fst · cited by 8CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.prodComparison_fst · cited by 8CartesianMonoidalCategory…CategoryTheory.CartesianMonoidalCategory.prodComparison_snd · cited by 8CartesianMonoidalCategory…CategoryTheory.Functor.Monoidal.μ_fst · cited by 7Monoidal.μ_fstCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.SemiCartesianMonoidalCategory · cited by 14CategoryTheory.SemiCartes…SemiCartesianMonoidalCategory…CITED BYCITES

Cites4

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Cited by224

Results whose statement or proof uses this declaration.