At the moment, I don’t think we’ve got a very good physical intuition for functors — just something which is completely and utterly abstracted away from the physical universe.

Well, we’ve got full image, essential image, and from optics a whole slew of machinery for dealing with images of things. Virtual images, focal depth, whatnot.

* Do functors have focal depth?

* Are there things which are not quite categories in which a functor could be diffracted?

* Think about imaging technologies: MRI, cat scans — anything which we use to construct visual representations of things might have a functorial analogue. Functorial holography? (and no, I don’t mean this: “holographic principle of higher category theory”

* Just how many of these w: optical phenomena have functorial analogues?

### Like this:

Like Loading...

*Related*

On the chora similarity blog the author mentions a squinty macro viewpoint on groups. Coarse spaces I think are related? There’s an AMS what is….? Article about it.

https://chorasimilarity.wordpress.com/2011/09/02/combinatorics-versus-geometric/#comment-10950

http://www.ams.org/notices/200606/whatis-roe.pdf

https://chorasimilarity.wordpress.com/2011/06/25/topological-substratum-of-the-derivative

web.stanford.edu/~ebwarner/KIDDIEtalk.pdf

Thinking it over, I don’t believe there’s much to say about functors. You either imbed one thing into another or cover one thing with another. That’s it, except for the isomorphic case. If theres something more interesting going on, like the imbedding spiderwebbing in a beautiful way, the covering entangling prettily, or the isomorphism swirling, any of this beauty would be captured in other non category theoretic terms. Like a Steiner system.

Maybe I’m missing something in the -expression- of each category, but I don’t think so.