One meaning (which is perhaps not so usual in math textbooks, but which you might encounter in the same kind of computer science literature where [monads] are popular) of the word '''algebraic''' is:
   * ''takes zero or more inputs, and produces exactly one output.''
Even transcendental functions are algebraic in this sense; what matters is only that what one wishes to express can be put in classical function-of notation, like f(g(x,y),h(z)).

The source for Tcl programs not employing side-effects ([upvar], [uplevel], etc.) are algebraic in this sense, because each individual command takes zero or more arguments, and produces exactly one result.

The prefix '''co-''' makes everything go backwards, so something is '''coalgebraic''' if it:
   * ''produces zero or more outputs, and has exactly one input.''
More generally, a notation for something can be coalgebraic if all fundamental components in it are coalgebraic.

Does such beasts actually exist in real life, though? Well, the traditional Unix composition in pipelines of many small programs that do simple things is ''kind of'' coalgebraic: the typical program has only [stdin] on the input side, but both [stdout] and [stderr] on the output side.

Flow diagrams are also sometimes considered as being coalgebraic. There is (in structured programming) only one place in which one can enter a block of code, but often several ways to leave it.

----
!!!!!!
%| [Category Concept] |%
!!!!!!