So, IIUC creating a NN basically follows this process:

- define an input vector space (i.e choose dimensions you want to operate on with input data)

- define your categories in another space (or another basis in the same space?)

- set up a transformation pipeline between the two spaces (with at least two stages)

- devise an algorithm that takes categorised elements and produces new transformation matrices

- train the NN (i.e feed input and categorise the result so that through some algorithm the transformation matrices converge)