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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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