motivated by the recent study on categorical properties of latticevalued topology, the paper considers a generalization of the notion of topological system introduced by s. vickers, providing an algebraic and a coalgebraic category of the new structures. as a result, the nature of the category   topsys   of s. vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalu...

Motivated by the recent study on categorical properties of latticevalued topology, the paper considers a generalization of the notion of topological system introduced by S. Vickers, providing an algebraic and a coalgebraic category of the new structures. As a result, the nature of the category   TopSys   of S. Vickers gets clari ed, and a metatheorem is stated, claiming that (latticevalu...

We define a notion of weak cubical category, abstracted from the structure of n-cubical cospans x : ∧ → X in a category X, where ∧ is the ‘formal cospan’ category. These diagrams form a cubical set with compositions x +i y in all directions, which are computed using pushouts and behave ‘categorically’ in a weak sense, up to suitable comparisons. Actually, we work with a ‘symmetric cubical struc...