Flux Can 2-Dimensional Input be fed into MLP columnwise for column output?

I have an MLP with one output and I am using Flux.
Is it possible to have an input of k columns of data and have each column applied to this same MLP so that the output is a column of size k?

If so, and if the above represents 1 training pattern, how might I represent a batch?

[Is this a special case of a Convolutional Network?]

Thanks for any help.