Theorems · Inductive type · category theory
CategoryTheory.SymmetricCategory
(C : Type u) → [inst : CategoryTheory.Category.{v, u} C] → [CategoryTheory.MonoidalCategory C] → Type (max u v)A symmetric monoidal category is a braided monoidal category for which the braiding is symmetric.
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 2 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement · cited by 32,673
- CategoryTheory.MonoidalCategorystatement · cited by 3,095
Cited by39
Results whose statement or proof uses this declaration.
- CategoryTheory.SymmetricCategory.symmetry_assocstatement and proof · cited by 11
- CategoryTheory.SymmetricCategory.symmetrystatement and proof · cited by 5
- CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.symmetricCategorystatement · cited by 4
- CategoryTheory.SymmetricCategory.braiding_swap_eq_inv_braidingstatement and proof · cited by 2
- CategoryTheory.GradedObject.Monoidal.symmetrystatement and proof · cited by 1
- CategoryTheory.symmetricOfHasFiniteCoproductsstatement · cited by 1
- CategoryTheory.SymmetricCategory.isMonoidalDistrib_of_isMonoidalLeftDistribstatement and proof · cited by 1
- CategoryTheory.SymmetricCategory.tensorμ_braid_swapstatement and proof · cited by 1
- CategoryTheory.Sheaf.symmetricCategorystatement and proof · cited by 0
- CategoryTheory.Monoidal.Reflective.closedstatement and proof · cited by 0
- CategoryTheory.Monoidal.Reflective.isIso_tfaestatement and proof · cited by 0
- CategoryTheory.Monoidal.Reflective.monoidalClosedstatement and proof · cited by 0