nLab
Mon(∞,1)Cat
Contents
Idea
The (∞,2)-category of monoidal (∞,1)-categories .

Variants
$\mathcal{O}$ -monoidal $(\infty,1)$ -category
A monoidal (∞,1)-category $(C, \otimes)$ is equivalently a coCartesian fibration of (∞,1)-operads over Assoc .

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

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

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

Properties
Model category presentations
see table - models for (infinity,1)-operads

Last revised on March 1, 2012 at 00:29:33.
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