From what I know, there is a vast literature on language recognizers in computer science. Language recognizers are machines (e.g., Finite State Automata, Pushdown Automata, Turing Machines, ...) that, for a given string of symbols, decide if the string belongs to a given language or not.
For my research, I need to study deterministic functions that map strings to strings, i.e., $f:\Sigma^*\to\Sigma^*$. I know that some models, like Turing Machines, can be "modified" to produce a sequence of output symbols.
Is there literature where I can find a categorization of machines that maps input string to output strings? I would like to know which models exist, and their categorization (e.g., something similar to the Chomsky classification)