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

The entries of the following table display models, model categories, and Quillen equivalences between these that present the (∞,1)-category of (∞,1)-categories (second table), of (∞,1)-operads (third table) and of $\mathcal{O}$-monoidal (∞,1)-categories (fourth table).

	general pattern
strict enrichment		(∞,1)-category/(∞,1)-operad
$\downarrow$		$\downarrow$
enriched (∞,1)-category	$\hookrightarrow$	internal (∞,1)-category
	(∞,1)Cat
SimplicialCategories	$-$homotopy coherent nerve$\to$	SimplicialSets/quasi-categories		RelativeSimplicialSets
$\downarrow$simplicial nerve		$\downarrow$
SegalCategories	$\hookrightarrow$	CompleteSegalSpaces
	(∞,1)Operad
SimplicialOperads	$-$homotopy coherent dendroidal nerve$\to$	DendroidalSets		RelativeDendroidalSets
$\downarrow$dendroidal nerve		$\downarrow$
SegalOperads	$\hookrightarrow$	DendroidalCompleteSegalSpaces
	$\mathcal{O}$Mon(∞,1)Cat
		DendroidalCartesianFibrations