Data di Pubblicazione:
2006
Citazione:
Injectivity and sections / F. Cagliari, S. Mantovani. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 204:1(2006), pp. 79-89.
Abstract:
We investigate injectivity
in a comma-category C/B using the notion of the "object of sections" S(f) of a given morphism f:X--> B in
C. We first obtain that f:X--> B is injective
in C/B if and only if the morphism
<1_X, f>:X--> XxB
is a section in C/B and the object S(f) of sections of
f is injective in C. Using this approach, we study
injective objects f with respect to the class of embeddings in
the categories ContL/B (AlgL/B)
of continuous (algebraic) lattices over B. As a
result, we obtain both topological (every fiber of f has
maximum and minimum elements and f is open and closed) and algebraic (f is a complete lattice homomorphism) characterizations.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
dcpo, Scott topology, exponentiable morphism,
partial product.
Elenco autori:
F. Cagliari, S. Mantovani
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