Theorems · Theorem · category theory
CategoryTheory.CommMon.mkIso.congr_simp
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
[inst_2 : CategoryTheory.BraidedCategory C] {M N : CategoryTheory.CommMon C} (e e_1 : M.X ≅ N.X) (e_e : e = e_1)
(one_f : CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.one e.hom = CategoryTheory.MonObj.one)
(mul_f :
CategoryTheory.CategoryStruct.comp CategoryTheory.MonObj.mul e.hom =
CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.tensorHom e.hom e.hom)
CategoryTheory.MonObj.mul),
CategoryTheory.CommMon.mkIso e one_f mul_f = CategoryTheory.CommMon.mkIso e_1 ⋯ ⋯- Defined in
- Mathlib.CategoryTheory.Monoidal.CommMon_
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
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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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Iso.homstatement and proof · cited by 7,684
- CategoryTheory.Isostatement and proof · cited by 3,963
- CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
- CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
- CategoryTheory.MonoidalCategoryStruct.tensorUnitstatement · cited by 1,384
- CategoryTheory.BraidedCategorystatement and proof · cited by 779
- CategoryTheory.MonoidalCategoryStruct.tensorHomstatement and proof · cited by 587
- CategoryTheory.MonObj.mulstatement and proof · cited by 230
- CategoryTheory.MonObj.onestatement and proof · cited by 189
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