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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.

Defined in
Mathlib.CategoryTheory.Monoidal.Braided.Basic
Cited by
19 results in Mathlib
Foundations
Depth 2 from the axioms · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.MonoidalCategory

Around this declaration

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

CategoryTheory.SymmetricCategory.symmetry_assoc · cited by 11SymmetricCategory.symmetr…CategoryTheory.SymmetricCategory.symmetry · cited by 5SymmetricCategory.symmetryCategoryTheory.MonoidalCategory.Arrow.PushoutProduct.symmetricCategory · cited by 4PushoutProduct.symmetricC…CategoryTheory.SymmetricCategory.braiding_swap_eq_inv_braiding · cited by 2SymmetricCategory.braidin…CategoryTheory.GradedObject.Monoidal.symmetry · cited by 1Monoidal.symmetryCategoryTheory.symmetricOfHasFiniteCoproducts · cited by 1CategoryTheory.symmetricO…CategoryTheory.SymmetricCategory.isMonoidalDistrib_of_isMonoidalLeftDistrib · cited by 1SymmetricCategory.isMonoi…CategoryTheory.SymmetricCategory.tensorμ_braid_swap · cited by 1SymmetricCategory.tensorμ…CategoryTheory.Sheaf.symmetricCategory · cited by 0Sheaf.symmetricCategoryCategoryTheory.Monoidal.Reflective.closed · cited by 0Reflective.closedCategoryTheory.Monoidal.Reflective.isIso_tfae · cited by 0Reflective.isIso_tfaeCategoryTheory.Monoidal.Reflective.monoidalClosed · cited by 0Reflective.monoidalClosedCategoryTheory.CopyDiscardCategory.mk.noConfusion · cited by 0mk.noConfusionCategoryTheory.GradedObject.Monoidal.symmetry_assoc · cited by 0Monoidal.symmetry_assocCategoryTheory.MonoidalCategory.DayConvolution.symmetry · cited by 0DayConvolution.symmetryCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.MonoidalCategory · cited by 3095CategoryTheory.MonoidalCa…CategoryTheory.SymmetricCateg…CITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by39

Results whose statement or proof uses this declaration.