Completing categorical algebras : Extended abstract
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 colimi...
Guardado en:
| Autores principales: | , |
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| Formato: | Objeto de conferencia |
| Lenguaje: | Inglés |
| Publicado: |
2006
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| Materias: | |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/24407 |
| Aporte de: |
| Sumario: | 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. |
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