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In this talk, we will present a model for infinity operads. We will start by discussing how the category of colored nonsymmetric operads can be embedded in a category which we call the category of simplicial lists. Within this category, our model for infinity operads will generalize colored nonsymmetric operads in the same way that quasicategories generalize ordinary categories when embedded in the category of simplicial sets. Therefore, it is natural to refer to these infinity operads as quasioperads. Next, we will discuss a homotopy coherent nerve functor from the category of simplicial operads to the category of simplicial lists, which sends Kan complex enriched operads to quasioperads, analogous to the homotopy coherent nerve functor from the category of simplicial categories to the category of simplicial sets. Finally, we will discuss the homology of simplicial lists, and hence quasioperads, and perform some homology computations.

This is joint work with Redi Haderi.

Zoom uygulaması Bilim Akademisi tarafından sağlanmaktadır./Zoom link is provided by The Science Academy.