Return to Revisions

As Peter said in a comment, "objectwise" is quite common and would probably be understood even without quotation marks, although it never hurts to define a term the first time you use it. I expect the reason that some people use "pointwise" is by analogy to functions between sets: the pointwise sum of $f,g:\mathbb{R}\to\mathbb{R}$ is $(f+g)(x)=f(x)+g(x)$, so the "pointwise tensor product" of $F,G:\mathcal{C}\to\mathcal{V}$ is $(F\otimes G)(C) = F(C) \otimes G(C)$.