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Title: A logic of implications in algebra and coalgebra
Authors: Adámek, Jirí 
Sobral, Manuela 
Sousa, Lurdes 
Issue Date: 2007
Publisher: Centro de Matemática da Universidade de Coimbra
Citation: Pré-Publicações DMUC. 07-15 (2007)
Abstract: Implications in a category can be presented as epimorphisms: an ob- ject satis¯es the implication i® it is injective w.r.t. that epimorphism. G. Ro»cu formulated a logic for deriving an implication from other implications. We present two versions of implicational logics: a general one and a ¯nitary one (for epimor- phisms with ¯nitely presentable domains and codomains). In categories Alg § 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.
Rights: openAccess
Appears in Collections:FCTUC Matemática - Vários

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