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...

The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley space...

This work expounds the notion that (structured) categories are syntax free presentations of type theories, and shows some of the ideas involved in deriving categorical semantics for given type theories. It is intended for someone who has some knowledge of category theory and type theory, but who does not fully understand some of the intimate connections between the two topics. We begin by showi...

A theory of how agents can come to understand a language is presented. If understanding a sentence α is to associate an operator with α that transforms the representational state of the agent as intended by the sender, then coming to know a language involves coming to know the operators that correspond to the meaning of any sentence. This involves a higher order operator that operates on the po...

We discuss ways in which category theory might be useful in philosophy of science, in particular for articulating the structure of scientific theories. We argue, moreover, that a categorical approach transcends the syntax-semantics dichotomy in 20th century analytic philosophy of science.

We give a sharper version of a theorem of Rosický, Trnková and Adámek [12], and a new proof of a theorem of Rosický [13], both about colimits in categories of structures. Unlike the original proofs, which use category-theoretic methods, we use set-theoretic arguments involving elementary embeddings given by large cardinals such as α-strongly compact and C(n)extendible cardinals.

We characterise quasivarieties and varieties of ordered algebras categorically in terms of regularity, exactness and the existence of a suitable generator. The notions of regularity and exactness need to be understood in the sense of category theory enriched over posets. We also prove that finitary varieties of ordered algebras are cocompletions of their theories under sifted colimits (again, i...

We present a category-theoretic approach to universal homogeneous objects, with applications in the theory of Banach spaces and in set-theoretic topology. Disclaimer: This is only a draft, full of gaps and inaccuracies, put to the Math arXiv for the sake of reference. More complete versions are coming soon.