Related papers: A constructive approach to the double-categorical …

The main goal of the present paper is two-fold. First we extend the theory of toroidal embeddings introduced by Kempf, Knudsen, Mumford and Saint-Donat to the class of toroidal varieties with stratifications (which is the main body of the…

We show that in a category with pullbacks, arbitrary sifted colimits may be constructed as filtered colimits of reflexive coequalizers. This implies that "lex sifted colimits", in the sense of Garner--Lack, decompose as Barr-exactness plus…

Positive modal logic was introduced in an influential 1995 paper of Dunn as the positive fragment of standard modal logic. His completeness result consists of an axiomatization that derives all modal formulas that are valid on all Kripke…

We establish a model structure on the category of strict omega-categories. The constructions leading to the model structure in question are expressed entirely within the scope of omega-categories, building on a set of generating…

We prove the (2,1)-categorical analogue of the small object argument and give a (2,1)-model structure on the category of small coherent categories, coherent functors and natural isomorphisms. It is induced by a higher dimensional example of…

A Quillen model structure is presented by an interacting pair of weak factorization systems. We prove that in the world of locally presentable categories, any weak factorization system with accessible functorial factorizations can be lifted…

We study a new type of higher categorical structure, called weakly globular n-fold category, previously introduced by the author. We show that this structure is a model of weak n-categories by proving that it is suitably equivalent to the…

We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…

We investigate the categories of weak maps associated to an algebraic weak factorisation system (AWFS) in the sense of Grandis-Tholen. For any AWFS on a category with an initial object, cofibrant replacement forms a comonad, and the…

The filter quotient construction is a particular instance of a filtered colimit of categories. It has primarily been considered in the context of categorical logic, where it has been used effectively to construct non-trivial models, for…

Definability is a key notion in the theory of Grothendieck fibrations that characterises when an external property of objects can be accessed from within the internal logic of the base of a fibration. In this paper we consider a…

We consider recognizable evaluations for a suitable category of oriented two-dimensional cobordisms with corners between finite unions of intervals. We call such cobordisms thin flat surfaces. An evaluation is given by a power series in two…

We construct the quantum s-tuple subfactors for an AFD II_1 subfactor with finite index and depth, for an arbitrary natural number s. This is a generalization of the quantum multiple subfactors by J.Erlijman and H.Wenzl, which generalizes…

Our aim is to construct fibrewise localizations in model categories. For pointed spaces, the general idea is to decompose the total space of a fibration as a diagram over the category of simplices of the base and replace it by the localized…

All rational semisimple braided tensor categories are representation categories of weak quasi Hopf algebras. To proof this result we construct for any given category of this kind a weak quasi tensor functor to the category of finite…

This thesis is devoted to the proof of a theorem showing the existence of a closed model category structure for weakly enriched categories. It requires first of all the definitions of weakly enriched categories and equivalences of weakly…

The concept of a weak factorization system has been studied extensively in homotopy theory and has recently found an application in one of the proofs of the celebrated flat cover conjecture, categorical versions of which have been presented…

We prove the following generalization of a classical result of Adams: for any pointed and connected topological space $(X,b)$, that is not necessarily simply connected, the cobar construction of the differential graded (dg) coalgebra of…

We introduce a new higher categorical structure called a weakly globular n-fold category. This structure is based on iterated internal categories and on the notion of weak globularity. We identify a suitable class of pseudo-functors whose…

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…