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) \( \otimes: C \times C \to C \).
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A monoidal category with natural invertible braidings satisfying the two hexagon axioms. The equation is an additional symmetric condition, not a braided axiom.