Data di Pubblicazione:
2007
Citazione:
Exponentiable monomorphisms in categories of domains / F. Cagliari, S. Mantovani. - In: JOURNAL OF PURE AND APPLIED ALGEBRA. - ISSN 0022-4049. - 211:2(2007 Nov), pp. 404-413.
Abstract:
We give a characterization of exponentiable monomorphisms in the categories ω-Cpo of ω-complete posets, Dcpo of directed
complete posets and ContD of continuous directed complete posets as those monotone maps f that are convex and that lift an
element (and then a queue) of any directed set (ω-chain in the case of ω-Cpo) whose supremum is in the image of f (Theorem
1.9). Using this characterization, we obtain that a monomorphism f : X → B in Dcpo (ω-Cpo, ContD) exponentiable in Top
w.r.t. the Scott topology is exponentiable also in Dcpo (ω-Cpo, ContD). We prove that the converse is true in the category ContD,
but neither in Dcpo, nor in ω-Cpo.
Tipologia IRIS:
01 - Articolo su periodico
Elenco autori:
F. Cagliari, S. Mantovani
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