We give a characterization of exponentiable monomorphisms in the categories omega-Cpo of omega-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 (omega-chain in the case of omega-Cpo) whose supremum is in the image of f. Using this characterization, we obtain that a monomorphism in Dcpo (omega-Cpo, ContD) exponentiable in Top w.r.t. the Scott topology is exponentiable also in Dcpo (omega-Cpo, ContD). We prove that the converse is true in the category ContD, but neither in Dcpo, nor inomega-Cpo.

F. Cagliari, S.Mantovani (2007). Exponentiable monomorphisms in categories of domains. JOURNAL OF PURE AND APPLIED ALGEBRA, 211, Issue 2, 404-413 [10.1016/j.jpaa.2007.02.004].

Exponentiable monomorphisms in categories of domains

CAGLIARI, FRANCESCA;
2007

Abstract

We give a characterization of exponentiable monomorphisms in the categories omega-Cpo of omega-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 (omega-chain in the case of omega-Cpo) whose supremum is in the image of f. Using this characterization, we obtain that a monomorphism in Dcpo (omega-Cpo, ContD) exponentiable in Top w.r.t. the Scott topology is exponentiable also in Dcpo (omega-Cpo, ContD). We prove that the converse is true in the category ContD, but neither in Dcpo, nor inomega-Cpo.
2007
F. Cagliari, S.Mantovani (2007). Exponentiable monomorphisms in categories of domains. JOURNAL OF PURE AND APPLIED ALGEBRA, 211, Issue 2, 404-413 [10.1016/j.jpaa.2007.02.004].
F. Cagliari; S.Mantovani
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/46901
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 3
social impact