By the way, the definition I'm using is the one from the nLab page: https://ncatlab.org/nlab/show/internal+category+in+a+monoidal+category On Sat, Oct 29, 2016 at 2:02 PM, Mike Stay <metaweta@gmail.com> wrote:
I'm having trouble understanding cotensors and the role they play in categories internal to a monoidal category.
Say we take the data from a category internal to Set and apply the "free complex-linear sums" functor to it. The result is not quite a category in Hilb, since the functor doesn't preserve limits: the product in Set gets mapped to the tensor product in Hilb. In particular, the composition function gets mapped to the composition linear transformation o: C^{Mor sxt Mor} -> C^Mor However, since we have a chosen basis, we can take a superposition of composable morphisms and produce a superposition of compositions.
Is this an example of a category internal to a monoidal category, and if so, is the Hilbert space C^{Mor sxt Mor} an example of a cotensor?
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
[For admin and other information see: http://www.mta.ca/~cat-dist/ ]
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com [For admin and other information see: http://www.mta.ca/~cat-dist/ ]