Having as starting point Barr’s description of topological spaces as lax algebras for the ultrafilter monad [2], in this paper we present further topological examples of lax algebras – such as quasi-metric spaces, approach spaces and quasi-uniform spaces – and show that, in a suitable setting, the categories of lax algebras have indeed a topological nature. Furthermore, we generalize to this se...

In this paper, we revisit topological-like features in the extended Temperley–Lieb diagrammatical representation for quantum circuits including the teleportation, dense coding and entanglement swapping. We perform these quantum circuits and derive characteristic equations for them with the help of topological-like operations. Furthermore, we comment on known diagrammatical approaches to quantum...

In this paper, we revisit topological-like features in the extended Temperley–Lieb diagrammatical representation for quantum circuits including the teleportation, dense coding and entanglement swapping. We perform these quantum circuits and derive characteristic equations for them with the help of topological-like operations. Furthermore, we comment on known diagrammatical approaches to quantum...

3 Motivic cohomology and algebraic cobordisms. 21 3.1 A topological lemma. . . . . . . . . . . . . . . . . . . . . . . . 21 3.2 Homotopy categories of algebraic varieties . . . . . . . . . . . 25 3.3 Eilenberg-MacLane spectra and motivic cohomology. . . . . . . 30 3.4 Topological realization functor. . . . . . . . . . . . . . . . . . . 33 3.5 Algebraic cobordisms. . . . . . . . . . . . . . . . ...

D. Molodtsov (1999) introduced the concept of a soft set as a new approach for modeling uncertainties. The aim of this work is to define special kinds of soft sets, namely soft, L-fuzzifying soft, L-soft, and L-fuzzy soft neighborhood sets and to use them in order to give an alternative characterization of categories related to topology: crisp topological, L-topological, L-fuzzifying topologica...