Is evidence that supports a witness's credibility relevant for impeachment purposes?

Evidence probative of a witness's credibility is relevant for impeachment purposes. (People v. Rodriguez (1999) 20 Cal.4th 1, 9.) "As with all relevant evidence, however, the trial court retains discretion to admit or exclude evidence offered for impeachment. [Citations.] 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]." (Id. at pp. 9-10.)