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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