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 |

Revised on March 14, 2012 05:44:26
by Urs Schreiber
(82.169.65.155)