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A coalgebraic semantics of subtyping

Erik Poll (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Coalgebras have been proposed as formal basis for the semantics of objects in the sense of object-oriented programming. This paper shows that this semantics provides a smooth interpretation for subtyping, a central notion in object-oriented programming. We show that different characterisations of behavioural subtyping found in the literature can conveniently be expressed in coalgebraic terms. We also investigate the subtle difference between behavioural subtyping and refinement.

A Coalgebraic Semantics of Subtyping

Erik Poll (2010)

RAIRO - Theoretical Informatics and Applications

Coalgebras have been proposed as formal basis for the semantics of objects in the sense of object-oriented programming. This paper shows that this semantics provides a smooth interpretation for subtyping, a central notion in object-oriented programming. We show that different characterisations of behavioural subtyping found in the literature can conveniently be expressed in coalgebraic terms. We also investigate the subtle difference between behavioural subtyping and refinement.

A coalgebraic view on reachability

Thorsten Wißmann, Stefan Milius, Shin-ya Katsumata, Jérémy Dubut (2019)

Commentationes Mathematicae Universitatis Carolinae

Coalgebras for an endofunctor provide a category theoretic framework for modeling a wide range of state-based systems of various types. We provide an iterative construction of the reachable part of a given pointed coalgebra that is inspired by and resembles the standard breadth-first search procedure to compute the reachable part of a graph. We also study coalgebras in Kleisli categories: for a functor extending a functor on the base category, we show that the reachable part of a given pointed coalgebra...

A cohomology theory for colored tangles

Carmen Caprau (2014)

Banach Center Publications

We employ the sl(2) foam cohomology to define a cohomology theory for oriented framed tangles whose components are labeled by irreducible representations of U q ( s l ( 2 ) ) . We show that the corresponding colored invariants of tangles can be assembled into invariants of bigger tangles. For the case of knots and links, the corresponding theory is a categorification of the colored Jones polynomial, and provides a tool for efficient computations of the resulting colored invariant of knots and links. Our theory is...

A construction of simplicial objects

Tomáš Crhák (2001)

Commentationes Mathematicae Universitatis Carolinae

We construct a simplicial locally convex algebra, whose weak dual is the standard cosimplicial topological space. The construction is carried out in a purely categorical way, so that it can be used to construct (co)simplicial objects in a variety of categories --- in particular, the standard cosimplicial topological space can be produced.

A construction of the Hom-Yetter-Drinfeld category

Haiying Li, Tianshui Ma (2014)

Colloquium Mathematicae

In continuation of our recent work about smash product Hom-Hopf algebras [Colloq. Math. 134 (2014)], we introduce the Hom-Yetter-Drinfeld category H H via the Radford biproduct Hom-Hopf algebra, and prove that Hom-Yetter-Drinfeld modules can provide solutions of the Hom-Yang-Baxter equation and H H is a pre-braided tensor category, where (H,β,S) is a Hom-Hopf algebra. Furthermore, we show that ( A ♮ ⋄ H , α ⊗ β ) is a Radford biproduct Hom-Hopf algebra if and only if (A,α) is a Hom-Hopf algebra in the category H H . Finally,...

Currently displaying 41 – 60 of 3011