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We've had a stub at representation for awhile; I rewrote it and let intertwiner redirect to it. But it's still a stub.
There is no difference, in their most general forms, between diagrams, representations, and functors.
But it's not that we're reinventing the wheel; rather, other people have reinvented the wheel already and we're recording when they use these terms and why.
Actions of beasts with many objects, e.g. categories, algebroids etc. involve anchor maps, anchor functors and alike. It is sometimes convenient to pack the whole gadget involving action into the action category involving both the acting category and acted upon entity. Maybe we should mention that point of view, often (among people near by) emphasised by Urs, Igor and others.
We have an old page action that should have this point of view mentioned on it.
Perhaps some very basic idea as to why representation theory of groups was thought up could be added. My recollection was that it was an attempt to use the well understood invariants of matrices, permutations etc, to obtain clearer information on abstract groups. We seem to have two views in the entry that instead of complementing each other (two faces of the same coin sort of thing) are pulling in slightly differing directions. Diagrams and representations are two names for the same things but form parts of different processes. A `DIAGRAM' somehow relates various different parts of a whole, whilst a representation more or less tries to explain one structure in terms of another.
Should we be trying to put forward something along these lines. I suspect there are aspects of `representations' that the above view ignores, so ... .
Should we be trying to put forward something along these lines.
Sure! Please go ahead and add this.
I have made a start. Please have a look and see if it does the job. I hope that we can link somewhere to the Café discussions on higher geometry higher actions, etc. and so I laid down some possible starts for later developments.
Okay, thanks!
I thought before the "Historical idea"-part we should have a real short plain "Idea"-part.
I have added a suggestion for that now. Maybe it is not quite a short as it should be. Have a look and feel free to take it apart.
I also edited the section layout a bit, rflecting the way how I think the entry seems to be developing.. See if you agree.
created stub for category of representations (and redirected: representation category)
While revising representation, don't forget that we also have representation theory.
Yes, I did think of that. But I don't feel yet in shape to give a good account there. We should ask David Ben-Zvi for a guest contribution here...
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