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### Sketches for categories of models of complete theories

In Accessible categories : the foundations of categorical model theory, chapter 3 p.58, Makkai and Paré claim that there is "an (obvious) identification of a class of sketches so that the categories ...

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### On Joyal's completeness theorem for first order logic

In 1978, in a series of unpublished conferences in Montréal, A. Joyal announced a remarkable theorem that unified several completeness theorems for fragments of first order logic, as well as first ...

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### Further relation between monads and theories

This question want to be a follow up of the following question.
In that thread I was interested in understanding relation between various presentation of algebraic theories. In particular in Eduardo ...

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### Category of Judgements?

I have been able to find a lot of information on the category of contexts -- for example, the page on syntactic categories at the nLab is a good starting point. However, when I try to find similar ...