Abstract
Motivated by a new approach in the categorical semantics of linear logic, we investigate some specific categories of coalgebras. They all arise from the canonical comonad that one has on a category of algebras. We obtain a very simple model of linear logic where linear formulas are complete lattices and intuitionistic formulas are just sets. Also, in another, domain theoretic example, we give a new characterization of continuous posets (where every elemtent is join of elements way below) as coalgebras. And finally we describe a related example where categories in which every object is coproduct of indecomposables, are coalgebras. Approximation is the key ingredient of all these coalgebras.
The research presented here was partly carried out during a visit to Sydney, supported by the Australian and Dutch research councils ARC and NWO.
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Jacobs, B. (1994). Coalgebras and approximation. In: Nerode, A., Matiyasevich, Y.V. (eds) Logical Foundations of Computer Science. LFCS 1994. Lecture Notes in Computer Science, vol 813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58140-5_18
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DOI: https://doi.org/10.1007/3-540-58140-5_18
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