Context

Higher algebra

higher algebra

universal algebra

Contents

Idea

A locally monoidal $(\infty,1)$-operad (called a coherent $(\infty,1)$-operad in (Lurie)) is an (∞,1)-operad $\mathcal{O}$ whose modules over $\mathcal{O}$-algebras come equipped with a well behaved tensor product

Definition

Definition

An (∞,1)-operad $\mathcal{O}^\otimes$ is locally monoidal if

1. it is unital;

2. the underlying (∞,1)-category $\mathcal{O}$ is an ∞-groupoid

3. (some third condition).

This is (Lurie, def. 3.3.1.9).

Examples

Locally monoidal $(\infty,1)$-operads include

References

Section 3.3.1 of

Last revised on February 11, 2013 at 18:15:10. See the history of this page for a list of all contributions to it.