Computational Category-Theoretic Rewriting

Category theoretic structure of setoids

A setoid is a set together with a constructive representation of an equivalencerelation on it. Here, we give category theoretic support to the notion. Wefirst define a category Setoid and prove it is cartesian closed with coproducts.We then enrich it in the cartesian closed category Equiv of sets and classicalequivalence relations, extend the above results, and prove that Setoid...

Presenting a Category Modulo a Rewriting System

Presentations of categories are a well-known algebraic tool to provide descriptions of categories by the means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations where the objects are considered modulo an equivalence relation (in the spirit of rewriting modulo), which is described by equational generators. When t...

Computational category theory

Information-theoretic approach to embodied category learning

We address the issue of how statistical and information-theoric measures can be employed to quantify the categorization process of a simulated robotic agent interacting with its local environment. We show how correlation, entropy, and mutual information can help identify distinct informational structure which can be used for object classification. Further, by means of the isometric feature mapp...

A Category Theoretic Model of RDF Ontology

Ontology languages are used in modelling the semantics of concepts within a particular domain and the relationships between those concepts. The Semantic Web standard provides a number of modelling languages that differ in their level of expressivity and are organized in a Semantic Web Stack in such a way that each language level builds on the expressivity of the other. There are several problem...