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Someone should improve this article so that it gives a definition of ‘algebraic theory’ before considering special cases such as ‘commutative algebraic theory’.
Thus is the current end to the entry on algebraic theory and I agree. Further I needed FP theory or FP sketch for something so looked at sketch. That looks as if it needs a bit of TLC as well, well not this afternoon as I have some other things that need doing. I did add the link to Barr and Wells, to sketch, however as this is now freely available as a TAC reprint.
and I agree
Me, too. On the other hand, notice that the entry Lawvere theory is considerably further developed.
The usual convention seems to be that Lawvere theories are generated by a single object, so are ’single sorted’. I need many sorted ones. Perhaps the redirect on algebras for an algebraic theory is not optimal. We can change it once there is a bit more meat in some of the relevant entries.
Yes, agreed. Eventually all this should be improved.
I was thinking of adapting stuff from Makkai and Paré on accessibility as it has a short intro to sketches, and then also to put in some thoughts on Toposes, Triples and Theories. (Perhaps a TOC for that book could be added somewhere. I will try to do it tonight. TAC did a reprint.)
(Edit later: Done the entry. A very stubby and the TOC is not elegantly formatted)
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