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Showing 1 to 3 of 3 for “"categorical logic"”.
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A DOCTRINAL VIEW OF LOGIC
The general framework of this thesis is Categorical Logic, more precisely the one of Doctrines, introduced by Lawvere in 1969. Doctrines are a categorical tool that allows the analysis of both syntax and semantics of logical theories — in particular first-order theories — using the same …
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The Dialectica Models of Type Theory
This thesis studies some constructions for building new models of Martin-Löf type theory out of old. We refer to the main techniques as gluing and idempotent splitting. For each we give general conditions under which type constructors exist in the resulting model. These techniques are used to …
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Infinitesimal Models of Algebraic Theories
… of an algebraic theory in cartesian logic. The last construction can be extended to first-order theories, which allows us to define infinitesimally euclidean and projective spaces, in principle. As regards the category of infinitesimal models of an algebraic theory in a Grothendieck …