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Another viewpoint on cartesian theories

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If you have a question about this talk, please contact Dr Ignacio Lopez Franco.

As is well known, cartesian theories have essentially the same expressive power as finite limit sketches, but some details are lost in the translation: for instance, a cartesian theory has an underlying algebraic theory, but this disappears after passing to the syntactic category. The gap can be bridged by introducing the notion of cartesian hyperdoctrine. Such a structure gives rise to a category of fibrant objects, and in the case of the cartesian hyperdoctrine generated by a cartesian theory T, its homotopy category is the syntactic category of T. The same construction also specialises to yield the reg/lex completion and the category of assemblies for a pca.

This talk is part of the Category Theory Seminar series.

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