nLab (∞,1)Operad

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Idea

The entries of the following table display 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

category: category

Last revised on October 30, 2012 at 14:25:19. See the history of this page for a list of all contributions to it.