Author(s):
Adámek, Jirí 
; Sobral, Manuela ; Sousa, Lurdes
Date: 2007
Persistent ID: http://hdl.handle.net/10316/11299
Origin: Estudo Geral - Universidade de Coimbra
Document details
A logic of implications in algebra and coalgebra
Description
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. Centre for Mathematics of University of Coim- bra/FCT; International Center for Mathematics; Ministry of Education of the Czech Republic, Project MSM 6840770014; School of Technology of Viseu
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. Centre for Mathematics of University of Coim- bra/FCT; International Center for Mathematics; Ministry of Education of the Czech Republic, Project MSM 6840770014; School of Technology of Viseu
Document Type
Preprint
Language English
Language English
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