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Journal

# Applied Categorical Structures

## Applied Categorical Structures OnlineFirst articles

16-10-2021

### Split Extensions and Actions of Bialgebras and Hopf Algebras

We introduce a notion of split extension of (non-associative) bialgebras which generalizes the notion of split extension of magmas introduced by M. Gran, G. Janelidze and M. Sobral. We show that this definition is equivalent to the notion of …

15-10-2021

### Pseudo-Dualizing Complexes of Bicomodules and Pairs of t-Structures

This paper is a coalgebra version of Positselski (Rendiconti Seminario Matematico Univ. Padova 143: 153–225, 2020) and a sequel to Positselski (Algebras and Represent Theory 21(4):737–767, 2018). We present the definition of a pseudo-dualizing …

30-08-2021

### Coends of Higher Arity

We specialise a recently introduced notion of generalised dinaturality for functors $$T : (\mathcal {C}^\mathsf {op})^p \times \mathcal {C}^q \rightarrow \mathcal {D}$$ T : ( C op ) p × C q → D to the case where the domain (resp., codomain) is …

06-08-2021

### Categorical Extension of Dualities: From Stone to de Vries and Beyond, I

Propounding a general categorical framework for the extension of dualities, we present a new proof of the de Vries Duality Theorem for the category KHaus of compact Hausdorff spaces and their continuous maps, as an extension of a restricted Stone …

02-08-2021

### Isbell Adjunctions and Kan Adjunctions via Quantale-Enriched Two-Variable Adjunctions

It is shown that every two-variable adjunction in categories enriched in a commutative quantale serves as a base for constructing Isbell adjunctions between functor categories, and Kan adjunctions are precisely Isbell adjunctions constructed from …