Full Subcategory: SymmMonCat ⊊ BrMonCat

SymmMonCat is a full subcategory of BrMonCat. When any two braided monoidal categories of BrMonCat are symmetric monoidal categories in SymmMonCat, all lax monoidal functors between them are lax monoidal functors in SymmMonCat too. Put another way, SymmMonCat has only some of the objects of BrMonCat, but all of the arrows.

In terms of stuff, structure, and properties, symmetric monoidal categories are like braided monoidal categories but with extra properties.

full_subcategories: SymmMonCat, BrMonCat

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