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