Abstract
A 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.
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