Related papers: Weak model categories in classical and constructiv…

The aim of this thesis is to give a concise introduction to homotopy type theory, to Aczel's constructive set theory and to simplicial sets and their homotopy theory in particular referring to their standard model structure, showing some of…

Weak values are average quantities,therefore investigating their associated variance is crucial in understanding their place in quantum mechanics. We develop the concept of a position-postselected weak variance of momentum as cohesively as…

Gambino and Garner proved that the syntactic category of a dependent type theory with identity types can be endowed with a weak factorization system structure, called identity type weak factorization system. In this paper we consider an…

The two model-theoretic concepts of weak saturation and weak amalgamation property are studied in the context of accessible categories. We relate these two concepts providing sufficient conditions for existence and uniqueness of weakly…

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 weak model category there are always Quillen equivalent…

If M is a model category and Z is an object of M, then there are model category structures on the category of objects of M over Z and the category of objects of M under Z under which a map is a cofibration, fibration, or weak equivalence if…

We give a potential alternative definition of a weak infinite dimensional category, in an unbiased fashion, using one one dimensional quiver with composition and extra structure.

Higher category theory is an exceedingly active area of research, whose rapid growth has been driven by its penetration into a diverse range of scientific fields. Its influence extends through key mathematical disciplines, notably homotopy…

We introduce relative homological and weakly homological categories, where ``relative'' refers to a distinguished class of normal epimorphisms. It is a generalization of homological categories, but also protomodular categories can be…

In this paper we study compact closed categories within the context of homotopical algebra. We construct two new model category structures by localizing two (Quillen equivalent) model categories of symmetric monoidal categories with the…

Interest in weak cubical n-categories arises in various contexts, in particular in topological field theories. In this paper, we describe a concept of double bicategory, namely a strict model of the theory of bicategories in Bicat. We show…

In this paper, we show that the Thomason model structure restricts to a Quillen equivalent cofibrantly generated model structure on the category of acyclic categories, whose generating cofibrations are the same as those generating the…

In this paper, we introduce a method to construct new categories which look like "cubes", and discuss model structures on the presheaf categories over them. First, we introduce a notion of thin-powered structure on small categories, which…

We develop abstract nonsense for module categories over monoidal categories (this is a straightforward categorification of modules over rings). As applications we show that any semisimple monoidal category with finitely many simple objects…

In previous work, we showed that there are appropriate model category structures on the category of simplicial categories and on the category of Segal precategories, and that they are Quillen equivalent to one another and to Rezk's complete…

We study the accessibility properties of trivial cofibrations and weak equivalences in a combinatorial model category and prove an estimate for the accessibility rank of weak equivalences. In particular, we show that the class of weak…

There is an ``algebraisation'' of the notion of weak factorisation system (w.f.s.) known as a natural weak factorisation system. In it, the two classes of maps of a w.f.s. are replaced by two categories of maps-with-structure, where the…

For a small simplicial category A, we prove that the homotopy colimit functor from the category of simplicial diagrams on A to the category of simplicial sets over the homotopy-coherent nerve of A provides a left Quillen equivalence between…

We attach to each weak model category $\mathcal{M}$ a class of first order formulas about the fibrant objects of $\mathcal{M}$ whose validity is invariant under homotopies and weak equivalences. This is a generalization of the classical…

We construct a model structure on the category $\mathrm{DblCat}$ of double categories and double functors, whose trivial fibrations are the double functors that are surjective on objects, full on horizontal and vertical morphisms, and fully…