We characterise the polarised evaluation order through a categorical structure where the hypothesis that composition is associative is relaxed. Duploid is the name of the structure, as a reference to Jean-Louis Loday’s duplicial algebras. The main result is a reflection Adj → Dupl where Dupl is a category of duploids and duploid functors, andAdj is the category of adjunctions and pseudo maps of...

We study 2-representations of finitary 2-categories with involution and adjunctions by functors on module categories over finite dimensional algebras. In particular, we define, construct and describe in detail (right) cell 2-representations inspired by KazhdanLusztig cell modules for Hecke algebras. Under some natural assumptions we show that cell 2-representations are strongly simple and do no...

The connection between constraints and universal algebra has been looked at in, and has given interesting results. Since the connection between universal algebra and category theory is so obvious, we will in this paper investigate if the usage of category theory has any impact on the results and/or reasoning and if anything can be gained from this approach. We construct categories of problem in...

We study comodule functors for comonads arising from mixed distributive laws. Their Galois property is reformulated in terms of a (so-called) regular arrow in Street’s bicategory of comonads. Between categories possessing equalizers, we introduce the notion of a regular adjunction. An equivalence is proven between the category of pre-torsors over two regular adjunctions (NA, RA) and (NB, RB) on...

For a small quantaloid $\mathcal{Q}$, it is shown that the category of $\mathcal{Q}$-distributors and diagonals equivalent to quotient $\mathcal{Q}$-interior spaces continuous $\mathcal{Q}$-distributors. Kan adjunctions induced by play crucial role in establishing this equivalence.

In this paper we show that there is no left adjoint to the inclusion functor from the full subcategory C 0 of Scott domains (i.e., consistently complete ! algebraic cpo's) to SFP, the category of SFP-objects and Scott-continuous maps. We also show there is no left adjoint to the inclusion functor from C 0 to any larger category of cpo's which contains a simple ve-element domain. As a corollary,...