'catalytically' originates from the English adjective 'catalytic' plus the adverbial suffix '-ally' (from Latin-derived '-al' + English '-ly'), where 'catalytic' relates to 'catalysis' (see below).

'catalytic' comes from the noun 'catalysis' (early 19th century), which was formed from Greek 'katalusis'/'katalysis' meaning 'a loosening' or 'dissolution'; the modern English adverb 'catalytically' developed by adding the productive English adverbial suffix '-ly' to 'catalytic'.

Initially, the Greek root referred to 'loosening' or 'dissolution'; over time it came to be used in chemistry to mean 'bringing about or accelerating a reaction (without being consumed)', and this specialized sense carried into the adjective and adverb forms ('catalytic', 'catalytically').