Publications
We further the study of the interactions between Reedy and monoidal structures on a small category, building upon the work of Barwick. In the second part, we study the category Nec of necklaces, as defined by Baues and Dugger-Spivak, showing that the category of A-valued presheaves on Nec is model monoidal when equipped with the Day convolution product, for any symmetric monoidal model category A.
We initiate the deformation theory of templicial modules. In particular, we show that two important classes of templicial modules, quasi-categories in modules and deg-projective templicial modules, are preserved under levelwise flat infinitesimal deformation.
Preprints
We construct a lift of Faonte's A-infinity-nerve which lands in templicial vector spaces. Further, we show that, when restricted to dg-categories, this nerve recovers the templicial dg-nerve and that the nerve of any A-infinity-category is a quasi-category in vector spaces.