nLab model structure for dendroidal left fibrations

Contents

Idea

The model structure for dendroidal left fibrations is an operadic analog of the model structure for left fibrations. Its fibrant objects over Assoc are A-∞ spaces, over Comm they are E-∞ spaces.

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For $f : S \to T$ any morphism of dendroidal sets, the induced adjunction (by Kan extension)

(f_! \dashv f^* ) : dSet/T \stackrel{\overset{f_!}{\leftarrow}}{\underset{f^*}{\to}} dSet/S

is a Quillen adjunction for the corresponding model structures for dendroidal left fibrations over $S$ and $T$ . It is a Quillen equivalence if $f$ is a weak equivalences in the Cisinki-Moerdijk model structure on dendroidal sets.

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The model structure for dendroidal left fibrations is due to

The model structure for dendroidal Cartesian fibrations that it arises from by Bousfield localization is due to

Last revised on March 7, 2012 at 10:42:57. See the history of this page for a list of all contributions to it.