Where does “catēchīzō” come from?

catēchīzō (Latin) comes from Ancient Greek κατηχίζω, from Ancient Greek κατήχησις, from Ancient Greek κατηχέω, from Ancient Greek κᾰτᾰ-, from Ancient Greek κατά, from Ancient Greek καταστερίζω, from Ancient Greek ἀστήρ, from Proto-Hellenic astḗr — to be/become dry; to burn, to glow; hearth.

Ancestry of “catēchīzō”, step by step

Step	Language	Word	Meaning
1	Ancient Greek	κατηχίζω	I instruct orally; to catechize
2	Ancient Greek	κατήχησις	oral instruction; instruction by word of mouth
3	Ancient Greek	κατηχέω	to resound; to teach by word of mouth
4	Ancient Greek	κᾰτᾰ-	fully; down; denoting motion downwards
5	Ancient Greek	κατά
6	Ancient Greek	καταστερίζω	to place among the stars; I put among the stars
7	Ancient Greek	ἀστήρ	a celestial body; illustrious person; starfish
8	Proto-Hellenic	astḗr	star
9	Proto-Indo-European	h₂stḗr	star
10	Proto-Indo-European	h₂eHs-	to be/become dry; to burn, to glow; hearth

Every word from Proto-Indo-European h₂eHs- →