nLab
Mon(∞,1)Cat

Contents

Idea

The (∞,2)-category of monoidal (∞,1)-categories.

Variants

𝒪\mathcal{O}-monoidal (,1)(\infty,1)-category

A monoidal (∞,1)-category (C,)(C, \otimes) is equivalently a coCartesian fibration of (∞,1)-operads over Assoc.

A symmetric monoidal (∞,1)-category (C,)(C, \otimes) is equivalently a coCartesian fibration of (∞,1)-operads over Comm.

Accordingly, for 𝒪\mathcal{O} any (∞,1)-operad, a coCartesian fibration of (,1)(\infty,1)-operads over 𝒪\mathcal{O} may be called an 𝒪\mathcal{O}-monoidal (,1)(\infty,1)-category.

OMon(,1)Cat:=coCart 𝒪. O Mon(\infty,1)Cat := coCart_{\mathcal{O}} \,.

Properties

Model category presentations

see table - models for (infinity,1)-operads

category: category

Revised on March 1, 2012 00:29:33 by Urs Schreiber (82.113.98.233)