What is relevant to the credibility of a witness who presents evidence for impeachment purposes?

nevertheless be relevant to the credibility of a witness who presents evidence on an issue; always relevant for impeachment purposes are the witness's capacity to observe and the existence or nonexistence of any fact testified to by the witness. (Evid. Code, 780, subds. (c), (i); [citation].) As with all relevant evidence, however, the trial court retains discretion to admit or exclude evidence offered for impeachment. (Evid. Code, 352; [citation].) A trial court's exercise of discretion in admitting or excluding evidence is reviewable for abuse [citation] and will not be disturbed except on a showing the trial court exercised its discretion in an arbitrary, capricious, or patently absurd manner that resulted in a manifest miscarriage of justice [citation]." (People v. Rodriguez (1999) 20 Cal.4th 1, 9-10.)