On Corelations, Cokernels, and Coequations

Abstract

In the paper we develop a new concept of specification for coalgebras strictly based on the duality between algebras and coalgebras.

We firstly present a systematic categorical analysis of basic concepts, constructions, and results in Universal Algebra. By a simple formal dualization we are able, in a second step, to present a kernel model theory of coalgebras for arbitrary functors T: Set → Set. Moreover, we are able to develop for functors T: Set → Set with cofree algebras a concept of coequational specification strictly dual to the concept of equational specification in Universal Algebra.