Wallace (GGBB, page 227) refers to the generic article as the "categorical article" which "distinguishes one class from another."
The key to identifying a generic article is by inserting the phrase "as a class" after the nominal word that the Greek article is modifying. So, ὁ ἄνθρωπος with a generic article would mean "humankind" (human beings as a class). This use of the article would set humanity apart from both animals and angels, which form distinct classes too. See Matthew 4:4.
One example that Wallace provides of the generic or categorical article is 1 Timothy 3:2, which reads (in part): "the overseer must be above reproach" (δεῖ οὖν τὸν ἐπίσκοπον ἀνεπίλημπτον εἶναι):
"Grammatically speaking, the article could either be monadic (indicating that for each church there is one overseer,) or it could be generic (indicating that overseers as a class are in view). When other considerations are brought to bear, however, it is unlikely that only one overseer is in view: (1) The monadic view cannot easily handle 1 Tim 5:17 ('let the elders who rule well be considered worthy of double honor') or Titus 1:5 ('appoint elders in every town'); and (2) the context of 1 Tim 2:8-3:16 involves an interchange of singular and plural generic nouns, suggesting strongly that the singular is used as a generic noun" (page 229).
Syntax of NT Greek (Brook and Winbery) also states:
"This use of the article is often referred to as the generic use. This use of the (definite) article may be translated as though the article were indefinite. Sometimes it may be best to translate a singular noun as though it were plural" (page 75).
Then examples such as Luke 10:7 are given along with 1 Timothy 3:2. Brooks and Winbery suggests "A bishop must be irreproachable" for the latter verse. See also Mt 18:17 and how the articles are employed there.