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Greek Anthology, Exhortative Epigrams 90

“Because he wanted to exercise his mind,
Homer made up the tale of frogs and mice,
Which he then gave to children to imitate.”

῞Ομηρος αὐτοῦ γυμνάσαι γνῶσιν θέλων,
τῶν βατράχων ἔπλασε καὶ μυῶν μῦθον
ἔνθεν παρορμῶν πρὸς μίμησιν τοὺς νέους.

The problematic biographies, the various Lives of Homer, include some similar information.

Vita Herodotea 332-4

“The man from Khios had children around the same age. They were entrusted to Homer for education. He composed these poems: the Kekropes, Batrakohmuomakia, Psaromakhia, Heptapaktikê, and Epikikhlides and as many other poems as were playful.”

ἦσαν γὰρ τῷ Χίῳ παῖδες ἐν ἡλικίῃ. τούτους οὖν αὐτῷ παρατίθησι παιδεύειν. ὁ δὲ ἔπρησσε ταῦτα· καὶ τοὺς Κέρκωπας καὶ Βατραχομυομαχίαν καὶ Ψαρομαχίην καὶ ῾Επταπακτικὴν καὶ ᾿Επικιχλίδας καὶ τἄλλα πάντα ὅσα παίγνιά ἐστιν.

Vita Plutarchea 1.98-100

“He wrote two poems, the Iliad and the Odyssey and, as some say, though not truthfully, he added the Batrakhomuomakhia and Margites for practice and education.”

ἔγραψε δὲ ποιήματα δύο, ᾿Ιλιάδα καὶ ᾿Οδύσσειαν, ὡς δέ τινες, οὐκ ἀληθῶς λέγοντες, γυμνασίας καὶ παιδείας ἕνεκα Βατραχομυομαχίαν προσθεὶς καὶ Μαργίτην.

Vita Quinta, 22-24

“Some also say that two school poems were attributed to him, the Batrakhomuomakhia and the Margites.”

τινὲς δ’ αὐτοῦ φασιν εἶναι καὶ τὰ φερόμενα δύο γράμματα, τήν τε Βατραχομυομαχίαν καὶ τὸν Μαργίτην.

The Margites is another epic parody we have only in fragmentary form.  Aristotle attributes it to Homer in his Poetics (1448b28-1449a3):

“We aren’t able to say anything about [parody] before Homer—but it is likely there were many—but we must start from Homer who leaves us the Margites and other works of this sort. It is fitting that among these works he also developed the iambic meter—for this is the very reason that iambos is called this today, since men are always mocking each other in that meter. Some of the ancient poets wrote heroic poetry, others wrote iambic.  Just as Homer was the exceptional poet in serious matters—for he didn’t only do it well in other ways but he also made his representations dramatic—in the same way he was the first to display the character of comedy in dramatizing something funny, not reproachful. And his Margites completes an analogy for us: just as the Iliad and the Odyssey are to tragedy, so to the Margites is to comedy.”

τῶν μὲν οὖν πρὸ ῾Ομήρου οὐδενὸς ἔχομεν εἰπεῖν τοιοῦτον ποίημα, εἰκὸς δὲ εἶναι πολλούς, ἀπὸ δὲ ῾Ομήρου ἀρξαμένοις ἔστιν, οἷον ἐκείνου ὁ Μαργίτης καὶ τὰ τοιαῦτα. ἐν οἷς κατὰ τὸ ἁρμόττον καὶ τὸ ἰαμβεῖον ἦλθε μέτρον—διὸ καὶ ἰαμβεῖον καλεῖται νῦν, ὅτι ἐν τῷ μέτρῳ τούτῳ ἰάμβιζον ἀλλήλους. καὶ ἐγένοντο τῶν παλαιῶν οἱ μὲν ἡρωικῶν οἱ δὲ ἰάμβων ποιηταί. ὥσπερ δὲ καὶ τὰ σπουδαῖα μάλιστα ποιητὴς ῞Ομηρος ἦν (μόνος γὰρ οὐχ ὅτι εὖ ἀλλὰ καὶ μιμήσεις δραμαικὰς ἐποίησεν), οὕτως καὶ τὸ τῆς κωμῳδίας σχῆμα πρῶτος ὑπέδειξεν, οὐ ψόγον ἀλλὰ τὸ γελοῖον δραματοποιήσας· ὁ γὰρ Μαργίτης ἀνάλογον ἔχει, ὥσπερ ᾿Ιλιὰς καὶ ἡ ᾿Οδύσσεια πρὸς τὰς τραγῳδίας, οὕτω καὶ οὗτος πρὸς τὰς κωμῳδίας.

The Batrakhomuomakhia, however, is not clearly ascribed to Homer until the first century CE.