6 papers
On categories of monads and comonads in double categories
Vasileios Aravantinos-Sotiropoulos, Theofilos Tsantilas, Christina Vasilakopoulou
As is well known in the literature, the category Mon(V) of monoids in a monoidal category V satisfies various fundamental categorical properties, at least when the monoidal base V…
Locales in presheaf toposes vs. presheaves of locales
Vasileios Aravantinos-Sotiropoulos, Panagis Karazeris, Joshua Wrigley
By a well-known characterisation, in a presheaf topos every internal suplattice is a presheaf of suplattices, but not every presheaf of suplattices is an internal suplattice (and s…
Poset-enriched categories and free exact completions
Vasileios Aravantinos-Sotiropoulos
We give an elementary construction of the exact completion of a weakly lex category for categories enriched in the cartesian closed category of partially ordered set…
Sweedler theory for double categories
Vasileios Aravantinos-Sotiropoulos, Christina Vasilakopoulou
In this work, we establish certain enrichments of dual algebraic structures in the setting of monoidal double categories. In more detail, we obtain a tensored and cotensored enrich…
The Exact Completion for Regular Categories enriched in Posets
Vasileios Aravantinos-Sotiropoulos
We construct an exact completion for regular categories enriched in the cartesian closed category of partially ordered sets and monotone functions by employing a sui…
Projective Covers of 2-star-permutable Categories
Vasileios Aravantinos-Sotiropoulos
We introduce the notion of star-symmetry for relations in a multi-pointed category and use it to obtain a characterization of the projective covers of 2-star-permutable categories.…