Centre for Mathematics, University of Coimbra

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Type:	Journal Article
National /International:	International
Title:	A logic of implications in algebra and coalgebra
Publication Date:	2009
Authors:	- Jirí Adámek - Manuela Sobral - Lurdes Sousa
Journal Name:	Algebra Universalis
Volume:	61
Number:	3-4
Pages:	313-337
Abstract:	Implications in a category can be presented as epimorphisms: an object satisfies the implication iff it is injective with respect to that epimorphism. G. Rosu formulated a logic for deriving an implication from other implications. We present two versions of implicational logics: a general one and a finitary one (for epimorphisms with finitely presentable domains and codomains). In categories Alg Σ of algebras on a given signature our logic specializes to the implicational logic of R. Quackenbush. In categories Coalg H of coalgebras for a given accessible endofunctor H of sets we derive a logic for implications in the sense of P. Gumm.
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