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Theorems · Theorem · category theory

CategoryTheory.MonObj.mul_eq_mul

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v, u_1} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  (M : C) [inst_2 : CategoryTheory.MonObj M],
  CategoryTheory.MonObj.mul =
    CategoryTheory.SemiCartesianMonoidalCategory.fst M M * CategoryTheory.SemiCartesianMonoidalCategory.snd M M
Defined in
Mathlib.CategoryTheory.Monoidal.Cartesian.Mon
Cited by
1 results in Mathlib
Foundations
Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonObj
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Around this declaration

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

CategoryTheory.isCommMonObj_iff_isMulCommutative · cited by 1CategoryTheory.isCommMonO…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.comp · cited by 17999CategoryStruct.compCategoryTheory.MonoidalCategoryStruct.tensorObj · cited by 3106MonoidalCategoryStruct.te…CategoryTheory.Category.id_comp · cited by 1998Category.id_compCategoryTheory.CartesianMonoidalCategory · cited by 947CategoryTheory.CartesianM…CategoryTheory.MonObj.mul · cited by 230MonObj.mulCategoryTheory.MonObj · cited by 199CategoryTheory.MonObjCategoryTheory.SemiCartesianMonoidalCategory.fst · cited by 184SemiCartesianMonoidalCate…CategoryTheory.SemiCartesianMonoidalCategory.snd · cited by 181SemiCartesianMonoidalCate…CategoryTheory.CartesianMonoidalCategory.lift · cited by 160CartesianMonoidalCategory…CategoryTheory.Hom.monoid · cited by 52Hom.monoidCategoryTheory.CartesianMonoidalCategory.lift_fst_snd · cited by 10CartesianMonoidalCategory…MonObj.mul_eq_mulCITED BYCITES

Cites13

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Cited by1

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