# Contents

## 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

category: category

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