We develop the concept of twisted ambidexterity in a parametrized presentably symmetric
monoidal $\infty $-category, which generalizes the notion of ambidexterity by Hopkins and …

We prove that for any presentably symmetric monoidal $\infty $-category $\mathcal {V} $, the
$\infty $-category $\mathbf {Mod} _\mathcal {V}(\mathbf {Pr}^{\mathrm {L}})^{\mathrm {dbl}} …

In this paper, we develop the notion of presentability in the parametrised homotopy theory
framework of Barwick et al.(Parametrized higher category theory and higher algebra: a …

The universal coCartesian fibration Page 1 arXiv:2210.08945v1 [math.CT] 17 Oct 2022 The
universal coCartesian fibration Denis-Charles Cisinski and Hoang Kim Nguyen Abstract. We …

Let $ X $ be a hypercomplete locally compact Hausdorff space and let $\mathcal C $ be a
compactly generated stable $\infty $-category. We describe the compact objects in the $\infty …

In this paper we will show that for a quasicompact quasiseparated scheme X the
hypercomplete pro-étale∞-topos, as introduced by Bhatt and Scholze, is equivalent to the∞ …

In this article, we introduce and develop the notion of parametrised Poincar\'{e} duality in the
formalism of parametrised higher category theory by Martini-Wolf, in part generalising …

We set the foundations of a theory of Grothendieck $(\infty, 2) $-topoi based on the notion of
fibrational descent, which axiomatizes both the existence of a classifying object for fibrations …

We advance the foundational study of be Nardin-Shah's $\infty $-category of $ G $-operads
and their associated $\infty $-categories of algebras. In particular, we construct the …

We establish abstract Adams isomorphisms in an arbitrary equivariantly presentable
equivariantly semiadditive global category. This encompasses the well-known Adams …