Related papers: Implications of a Quillen Model Structures-Based F…
We prove a localisation theorem for the K-theory of filtering subcategories of exact $\infty$-categories which subsumes the localisation theorem for stable $\infty$-categories, Quillen's localisation theorem for abelian categories, and…
Local consistency arises in diverse areas, including Bayesian statistics, relational databases, and quantum foundations, and so does the notion of functional dependence. We adopt a general approach to study logical inference in a setting…
We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…
We lift Charles Rezk's complete Segal space model structure on the category of simplicial spaces to a Quillen equivalent one on the category of relative categories.
We introduce and compare two approaches to equivariant homotopy theory in a topological or ordinary Quillen model category. For the topological model category of spaces, we generalize Piacenza's result that the categories of topological…
This article is an exploratory account of the the non-monotonic behaviour of conceptual associations in the light of context. Computational approximations of conceptual space are furnished by semantic space models which are emerging from…
Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories M(s) (as s runs through the diagram), we…
We show under mild hypotheses that a Quillen adjunction between stable model categories induces another Quillen adjunction between their left localizations, and we provide conditions under which the localized adjunction is a Quillen…
We investigate under which assumptions a subclass of flat quasi-coherent shea\-ves on a quasi-compact and semi-separated scheme allows to "mock" the homotopy category of projective modules. Our methods are based on module theoretic…
The homotopy theory of representations of nets of algebras over a (small) category with values in a closed symmetric monoidal model category is developed. We illustrate how each morphism of nets of algebras determines a change-of-net…
We show that weak monoidal Quillen equivalences induce equivalences of symmetric monoidal $\infty$-categories with respect to the Dwyer-Kan localization of the symmetric monoidal model categories. The result will induce a Dold-Kan…
We explore the interlacing between model category structures attained to classes of modules of finite $\mathcal{X}$-dimension, for certain classes of modules $\mathcal{X}$. As an application we give a model structure approach to the…
We show that a category $\mathscr{M}$ equipped with a model structure defined by a proper, locally small class of orbits $\mathscr{O}$ is Quillen equivalent to the category of small relative presheaves…
If all objects of a simplicial combinatorial model category \cat A are cofibrant, then there exists the homotopy model structure on the category of small functors $\sS^{\cat A}$, where the fibrant objects are homotopy functors, i.e.,…
This paper develops a {\em qualitative} and logic-based notion of similarity from the ground up using only elementary concepts of first-order logic centered around the fundamental model-theoretic notion of type.
Predicate logic is the premier choice for specifying classes of relational structures. Homomorphisms are key to describing correspondences between relational structures. Questions concerning the interdependencies between these two means of…
We give sufficient conditions for the existence of a Quillen model structure on small categories enriched in a given monoidal model category. This yields a unified treatment for the known model structures on simplicial, topological, dg- and…
The reasoning with qualitative uncertainty measures involves comparative statements about events in terms of their likeliness without necessarily assigning an exact numerical value to these events. The paper is divided into two parts. In…
In [Homotopical Algebra, Springer LNM 43] Quillen introduces the notion of a model category: a category $\mathcal{C}$ provided with three distinguished classes of maps $\{\mathcal{W},\, \mathcal{F},\, co\mathcal{F}\}$ (weak equivalences,…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…