On Minimal Coalgebras

Abstract. We define an out-degree for F-coalgebras and show that the coalgebras of outdegree at most form a covariety. As a subcategory of all Fcoalgebras, this class has a terminal object, which for many problems can stand in for the terminal F-coalgebra, which need not exist in general. As examples, we derive structure theoretic results about minimal coalgebras, showing that, for instance minimization of coalgebras is functorial, that products of finitely many minimal coalgebras exist and are given by their largest common subcoalgebra, that minimal subcoalgebras have no inner endomorphisms and show how minimal subcoalgebras can be constructed from Moore-automata. Since the elements of minimal subcoalgebras must correspond uniquely to the formulae of any logic characterizing observational equivalence, we give in the last section a straightforward and self-contained account of the coalgebraic logic of D. Pattinson and L. Schr

• Type: Journal
• Year: 2008
• Where: ACS
• Authors: H. Peter Gumm
• Keywords: ACS 2008, Distributed And Parallel Computing, Largest Common Subcoalgebra, Minimal Coalgebras, Minimal Subcoalgebras