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This is a brief introduction to link homology theories that categorifyReshetikhin--Turaev $\mathsf{SL}(N)$-quantum link invariants. A recentlydiscovered surprising connection between finite state automata and BooleanTQFTs in dimension one is explained as a warm-up.

From finite state automata to tangle cobordisms: a TQFT journey from one to four dimensions