We prove the conjecture that any Grothendieck $(\infty, 1) $-topos can be presented by a
Quillen model category that interprets homotopy type theory with strict univalent universes …

The idea for this book was conceptualized during a research visit to Macquarie University in
the summer of 2017. At first, I was interested in collecting exotic examples of model …

We construct a refinement of Gaitsgory's central functor for integral motivic sheaves, and
show it preserves stratified Tate motives. Towards this end, we develop a reformulation of …

In the enriched setting, the notions of injective and projective model structures on a category
of enriched diagrams also make sense. In this paper, we prove the existence of these model …

In this paper we establish Koszul duality between dg categories and a class of curved
coalgebras, generalizing the corresponding result for dg algebras and conilpotent curved …

In a previous work, we have introduced a weakening of Quillen model categories called
weak model categories. They still allow all the usual constructions of model category theory …

We construct a model structure on the category $\mathrm {DblCat} $ of double categories
and double functors. Unlike previous model structures for double categories, it recovers the …

We construct a q-model structure, a h-model structure and a m-model structure on
multipointed $ d $-spaces and on flows. The two q-model structures are combinatorial and …

Let $ P $ be a poset. We define a new homotopy theory of suitably nice $ P $-stratified
topological spaces with equivalences on strata and links inverted. We show that the exit …

We introduce the notion of a braiding on a skew monoidal category, whose curious feature is
that the defining isomorphisms involve three objects rather than two. These braidings are …