nLab braided monoidal (∞,1)-category

Definition

Where a monoidal (∞,1)-category is an E1-algebra in (∞,1)Cat, a braided monoidal $(\infty,1)$-category is an E2-algebra in (∞,1)Cat.

If the (∞,1)-category $\mathcal{C}$ underlying a braided monoidal $(\infty,1)$-category $(\mathcal{C}, \otimes)$ is a 1-category, then $(\mathcal{C}, \otimes)$ is a braided monoidal category.

Related concepts

• monoidal category, monoidal (∞,1)-category

• braided monoidal category, braided monoidal $(\infty,1)$-category

  • braided ∞-group

• symmetric monoidal category, symmetric monoidal (∞,1)-category

• closed monoidal category , closed monoidal (∞,1)-category