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.
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.
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.