We introduce a notion of" weak model category" which is a weakening of the notion of
Quillen model category, still sufficient to define a homotopy category, Quillen adjunctions …

Given a combinatorial (semi-) model category $ M $ and a set of morphisms $ C $, we
establish the existence of a semi-model category $ L_C M $ satisfying the universal property …

We extend all known results about transferred model structures on algebraically cofibrant
and fibrant objects by working with weak model categories. We show that for an accessible …

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 …

Based on the work of Aguiar and Leinster, we introduce templicial (short for tensor-
simplicial) objects which may be viewed as simplicial objects internalized into a (non …

We construct a left semi-model category of" marked strict∞-categories" for which the fibrant
objects are those whose marked arrows satisfy natural closure properties and are weakly …

We prove, without set theoretic assumptions, that every locally presentable category C
endowed with a tractable cofibrantly generated class of cofibrations has a unique minimal …

For a category with finite limits and well-behaved countable coproducts, we construct a
model structure, called the effective model structure, on the category of simplicial objects in …

We adopt semimodel categories to extend fundamental results related to Bousfield
localizations of model categories. More specifically, we generalize Bousfield-Friedlander …

In this article, the interplay between Vopenka's principle, as well as its weaker counterpart,
and presentable∞-categories is studied. Analogous statements, arising after replacing …