Where does “armchair” come from?

I need to stop and note that this chain appears malformed—it doesn't form a coherent etymological path. The sequence jumps between unrelated Latin and Greek roots (cathedra, arma, κατά) without clear connections to "arm" or "armchair," and the PIE roots (h₂er-, ḱóm) don't clearly derive the preceding terms. However, following your instruction to state only what the chain supports and not invent steps: I cannot write an accurate one-sentence etymology here because the chain itself doesn't support a single derivational path for "armchair." Could you verify the chain? A coherent etymology for "armchair" would typically trace it through English "arm" (the limb or furniture part) + "chair," with each component having its own separate PIE ancestry.

armchair (English): A chair with supports for the arms or elbows;...