Related papers: Fibrancy of Partial Model Categories
We gather conditions on a class H of continuous maps of topological spaces that allow a reasonable theory of fibrations up to an equivalence (a map from this class) which we call H-fibrations. The weak homotopy equivalences recover…
Fiber functors on Temperley-Lieb categories are investigated with the help of classification results on non-degenerate bilinear forms. The case of unitary fiber functors is also considered.
Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…
We introduce cohomology and homology theories for small categories with general coefficient systems from simplex categories first studied by Thomason. These theories generalize at once Baues-Wirsching cohomology and homology and other more…
In this paper we propose an approach to homotopical algebra where the basic ingredient is a category with two classes of distinguished morphisms: strong and weak equivalences. These data determine the cofibrant objects by an extension…
We prove that a weak factorization system on a locally presentable category is accessible if and only if it is small generated in the sense of R. Garner. Moreover, we discuss an analogy of Smith's theorem for accessible model categories.
We study the local isomorphism classes, also known as genera or weak equivalence classes, of fractional ideals of orders in \'etale algebras. We provide a classification in terms of linear algebra objects over residue fields. As a…
This article is a sequel to hep-th/9411050, q-alg/9412017. In Chapter 1 we associate with every Cartan matrix of finite type and a non-zero complex number $\zeta$ an abelian artinian category $\FS$. We call its objects {\em finite…
We introduce fibred type-theoretic fibration categories which are fibred categories between categorical models of Martin-L\"{o}f type theory. Fibred type-theoretic fibration categories give a categorical description of logical predicates…
In this note we describe conditions under which the algebras for a monad on a presheaf category equipped with some additional structure are fibrant objects in a model structure. We also prove that when these conditions are satisfied the…
Taking matrix as a synonym for a numerical function on the Cartesian product of two (in general, infinite) sets, a simple purely algebraic "reciprocity property" says that the set of rows spans a finite-dim space iff the set of columns does…
We define a notion of a weak canonical base for a partial type. This notion is weaker than the usual canonical base for an amalgamation base. We prove that certain family of partial types have a weak canonical base. This family clearly…
We show that a map between fibrant objects in a closed model category is a weak equivalence if and only if it has the right homotopy extension lifting property with respect to all cofibrations. The dual statement holds for maps between…
In this article, we construct a cofibrantly generated Quillen model structure on the category of small topological categories $\mathbf{Cat}_{\mathbf{Top}}$. It is Quillen equivalent to the Joyal model structure of $(\infty,1)$-categories…
We formulate the concept of minimal fibration in the context of fibrations in the model category $\mathbf{S}^\mathcal{C}$ of $\mathcal{C}$-diagrams of simplicial sets, for a small index category $\mathcal{C}$. When $\mathcal{C}$ is an…
We study when the stable category of an abelian category modulo a full additive subcategory is balanced and, in case the subcategory is functorially finite, we study a weak version of balance. Precise necessary and sufficient conditions are…
We show that the fibrant objects in the minimal model structure on the category of simplicial sets are characterized by a lifting condition with respect to maps which resemble the horn inclusions that define Kan complexes.
We establish that a category of fibrant objects (in the sense of Brown) admits a Dwyer-Kan homotopical calculus of right fractions. This is done using a homotopical calculus of cocycles, which is an auxiliary structure that can be defined…
We construct a left semi-model category of "marked strict $\infty$-categories" for which the fibrant objects are those whose marked arrows satisfy natural closure properties and are weakly invertible. The canonical model structure on strict…
We prove the well-definedness of some deformations of the fibred biset category in characteristic zero. The method is to realize the fibred biset category and the deformations as the invariant parts of some categories whose compositions are…