Where does “katalógusok” come from?

katalógusok (Hungarian) comes from Hungarian katalógus, from Latin catalogus, from Ancient Greek κατάλογος, from Ancient Greek καταλέγω, from Ancient Greek κᾰτᾰ-, from Ancient Greek κατά, from Ancient Greek καταστερίζω, from Ancient Greek ἀστήρ — to be/become dry; to burn, to glow; hearth.

Ancestry of “katalógusok”, step by step

Step	Language	Word	Meaning
1	Hungarian	katalógus	catalogue, catalog
2	Latin	catalogus	catalogue
3	Ancient Greek	κατάλογος	enrolment; register, catalogue
4	Ancient Greek	καταλέγω	to pick out, to choose out of, to...
5	Ancient Greek	κᾰτᾰ-	fully; down; denoting motion downwards
6	Ancient Greek	κατά
7	Ancient Greek	καταστερίζω	to place among the stars; I put among the stars
8	Ancient Greek	ἀστήρ	a celestial body; illustrious person; starfish
9	Proto-Hellenic	astḗr	star
10	Proto-Indo-European	h₂stḗr	star
11	Proto-Indo-European	h₂eHs-	to be/become dry; to burn, to glow; hearth

Every word from Proto-Indo-European h₂eHs- →Every word from Proto-Indo-European h₂stḗr →Every word from Proto-Hellenic astḗr →