Operators on classes of coalgebras

AbstractA class K of T-coalgebras is called a covariety if K=SHΣ(K). SHΣ is just one of several class operators which can be formed by composing H,S and Σ. In this paper, we show that starting from H,S and Σ one can form exactly 13 different class operators (including the operator I of taking the isomorphic copies). We first describe the partially ordered monoid generated by these three operators for the class of all functors Set→Set, then for the class of all functors preserving weak pullbacks along injective mappings, and finally, for particular functors from a rather large class which includes all non-constant polynomial functors