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Types and coalgebraic structure. (English) Zbl 1086.08002
Summary: We relate weak limit preservation properties of coalgebraic type functors \(F\) to structure-theoretic properties of the class \(\mathcal Set_F\) of all \(F\)-coalgebras. In particular, we give coalgebraic characterizations for the condition that \(F\) weakly preserves pullbacks, kernel pairs or preimages. We also describe regular monos and epis. In case that \(| F| \not= 1\) we show that \(F\) preserves preimages iff \(\mathcal{HS}(\mathcal K) = \mathcal{SH}(\mathcal K)\) for every class \(\mathcal K\) of \(F\)-coalgebras. The case \(| F(1)| = 1\) is left as an open problem.

08A70 Applications of universal algebra in computer science
18A35 Categories admitting limits (complete categories), functors preserving limits, completions
18B20 Categories of machines, automata
68Q65 Abstract data types; algebraic specification
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