A monoidal category with natural invertible braidings satisfying the two hexagon axioms. The equation is an additional symmetric condition, not a braided axiom.
The braided monoidal category generated by one object: objects are parenthesized tensor expressions in that object and the unit, and morphisms are structural isomorphisms and crossings subject to precisely the monoidal category and braiding axioms.
The braided monoidal category with objects , endomorphism groups , no arrows between unequal objects, tensor given by juxtaposition, and block-crossing braiding. Its tensor is strict.
The natural tensor interchange isomorphism in a braided monoidal category, constrained by the two hexagon axioms.
Articles by others on the same topic
A *braided monoidal category* is a particular type of category that combines the structure of a monoidal category with a braiding. To understand this structure, let's unpack a few key concepts. 1. **Monoidal Category**: A monoidal category consists of: - A category \( C \). - A tensor product (a bifunctor) \( \otimes: C \times C \to C \).