Algebra, Logic and Topology

 

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Author(s)
Jirí Adámek; Lurdes Sousa; Manuela Sobral;

Title
A logic of implications in algebra and coalgebra

Abstract
Implications in a category can be presented as epimorphisms: an object satisfies the implication iff it is injective w.r.t. that epimorphism. G. Roçu 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 \Sigma 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.

Preprint series
Pré-publicações do Departamento de Matemática da Universidade de Coimbra

Issue
07-15

Year
2007

 
     
 

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