Mathematical equivalent of reduce()?

Question

filter() in functional programming can be thought of as being analogous to an equation that filters the range of the variable.

map() can be through of as a function mapping domain to codomain.

reduce() is the only one I have a problem with. To me it just seems to be a special instance of map / function, where $R^{n} \rightarrow R^{1}$.

Is there a unique general mathematical concept / object associated with reduce()?