# Meaning of “parallel” in the context of arrows and functions (category theory)

I haven't been able to find an explanation of the term "parallel" in the context of (category theory) arrows and functions.

For example, in the statement "given arrows f and g with domain A and codomain B" are f and g necessarily considered to be "parallel arrows"? Or, would the addition of the word "parallel" (as in "given parallel arrows f and g with domain A and codomain B") indicate some additional semantics of f and g?

In the context of category theory, I sometimes see the same terminology applied to functions as well. I assume the term "parallel" has the same meaning for functions in this context, but would like to be sure.

Edit: In looking back over the examples of "parallel functions" (in Topoi and Category Theory in Context) I notice that they are used primarily in examples of the Set category and occasionally in other categories where the arrows represent functions. The surrounding discussion does not seem to use any other qualities of these functions other than their domain and codomain. Therefore, to update the second half of the question:

In the context of a category where the arrows are functions, does "parallel functions" have the same meaning as "parallel arrows?" If not, can you give an example of a category where the term "parallel functions" conveys more information than both functions have the same domain and both functions having the same codomain?

• "Parallel" here means "same domain and same codomain" so yes to your first question, no to the second one – Max Feb 2 '18 at 15:43