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I pasted in something Mike wrote on sketches and accessible models to sketch. But now it needs tidying up, and I’m wondering if it might have been better placed at accessible category. Alternatively we start a new page on sketch-theoretic model theory. Ideas?
Putting it at accessible category sounds good to me.
Added a small idea section and an example.
Andrée Ehresmann pointed out on the catlist that our definition of sketch was actually the definition of a realized sketch, so I fixed our page to the more general version.
The category of sketches has a well behaved symmetric monoidal structure that can be useful when discussing models of theories inside of models of theories, such as double categories or vector bundle groupoids. I thought it might be useful to have on the nlab page for sketches.
Ben MacAdam
Was intending just to do a little tidying and book-keeping, but ended up rewriting the idea section as well, and giving, for my sins, the full details of a couple of examples; writing down the full details of a sketch in practise is a little more subtle than one might think if one has not tried it.
added pointer to:
In the previous version it was claimed that the tensor product of sketches was part of a symmetric monoidal structure on the category of sketches. That is wrong. I sketched the right statement (factors in the tensor product can be swapped if the specified limits and colimits commute), gave a reference, and gave an example (I think) where one can not switch the factors.
Peter Arndt
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