nLab
locally monoidal (infinity,1)-operad

Contents

Idea

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

Definition

Definition

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

  1. it is unital;

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

  3. (some third condition).

This is (Lurie, def. 3.3.1.9).

Examples

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

References

Section 3.3.1 of

Revised on February 11, 2013 18:15:10 by Urs Schreiber (89.204.138.151)