To be super clear, the quoted sentence continues, including the typeset formula below it. (It's an academic convention that I'm not a particular fan of.) > Pro

To be super clear, the quoted sentence continues, including the typeset formula below it. (It's an academic convention that I'm not a particular fan of.) > Product is functorial in both arguments so, in particular, we can define a functor L_a(c) = c * a. Bartosz is saying that we can fix one side of the product, giving us a one-argument specialization that is a functor. In this case, we're fixing `a` (subscript binds tighter than parameters, in some sense) and letting `c` vary. That's what it means to be functorial in both arguments: fix either one and you get a functor. The same phenomenon shows up in other fields where you have n-ary functions. Bilinear maps (in linear algebra) are linear in each argument. You could come up with something similar involving continuity in each argument for a binary function in real analysis (although I think that would actually be a weaker property than claiming the binary function is continuous...)