Algebraic topological methods have been used successfully in concurrency theory, the domain of theoretical computer science that deals with parallel computing. L. Fajstrup, E. Goubault, and M. Raussen have introduced partially ordered spaces (pospaces) as a model for concurrent systems. In this paper it is shown that the category of pospaces under a fixed pospace is both a fibration and a cofib...

We prove that the existence of arbitrarily large supercompact cardinals implies that every absolute epireflective class of objects in a balanced accessible category is a small-orthogonality class. In other words, if L is a localization functor on a balanced accessible category such that the unit morphism X → LX is an epimorphism for all X and the class of L-local objects is defined by an absolu...

In a previous work, we gave a coalgebraic framework of directed graphs equipped with weights (or probability vectors) in terms of (Markov) L-coalgebras. They are K-vector spaces equipped with two co-operations, ∆M , ∆̃M verifying, (∆̃M ⊗ id)∆M = (id⊗∆M)∆̃M . In this paper, we study the category of L-algebras (dual of L-coalgebras), prove that the free L-algebra on one generator is constructed over...

This paper introduces a new approach to the theory of Ω-categories enriched by a frame. The approach combines ideas from various areas such as generalized ultrametric domains, Ω-categories, constructive analysis, and fuzzy mathematics. As the basic framework, we use the Wagner’s Ω-category [18,19] with a frame instead of a quantale with unit. The objects and morphisms in the category will be ca...

Throughout this note G denotes a discrete group. A G-complex is a CPP-complex on which G acts by cellular maps such that the fixed point set of any element of G is a subcomplex. On the category of pairs of G-complexes and equivariant homotopy classes of maps, an equivariant cohomology theory is a sequence of contravariant functors 3C into the category of abelian groups together with natural tra...

In the theory of dynamical Yang-Baxter equation, with any Hopf algebra H and a certain H-module and H-comodule algebra L (base algebra) one associates a monoidal category. Given an algebra A in that category, one can construct an associative algebra A⋊L, which is a generalization of the ordinary smash product when A is an ordinary H-algebra. We study this ”dynamical smash product” and its modul...

We pose the problem of whether every FS-domain is a retract of abifinite domain purely in terms of quasi-uniform spaces. 6.1 The problem and its historyEver since domains were introduced by Dana Scott [Sco70] and Yuri Er-shov [Ers75], a question in the centre of interest was to find suitable cartesianclosed categories of domains and the quest for cartesian closed categories ...