Completing categorical algebras : Extended abstract

• Autores: Bloom, Stephen L.; Esik, Zoltán
• Año de publicación: 2006
• Idioma: inglés
• Tipo de recurso: documento de conferencia
• Materia: Ciencias Informáticas; categorical algebras
• Institución: Universidad Nacional de La Plata

Let Σ be a ranked set. A categorical Σ-algebra, cΣa for C, for short, is a small category C equipped with a functor σC : C n each σ ∈ Σn , n ≥ 0. A continuous categorical Σ-algebra is a cΣa which C; has an initial object and all colimits of ω-chains, i.e., functors N each functor σC preserves colimits of ω-chains. (N is the linearly ordered set of the nonnegative integers considered as a category as usual.) We prove that for any cΣa C there is an ω-continuous cΣa C ω , unique up to equivalence, which forms a “free continuous completion” of C. We generalize the notion of inequation (and equation) and show the inequations or equations that hold in C also hold in C ω . We then find examples of this completion when – C is a cΣa of finite Σ-trees – C is an ordered Σ algebra – C is a cΣa of finite A-sychronization trees – C is a cΣa of finite words on A.
4th IFIP International Conference on Theoretical Computer Science
Red de Universidades con Carreras en Informática (RedUNCI)