Isomorphism within Naive Type Theory

David McAllester

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arXiv · 1407.7274

Isomorphism within Naive Type Theory

David McAllester

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Abstract

We provide a treatment of isomorphism within a set-theoretic formulation of dependent type theory. Type expressions are assigned their natural set-theoretic compositional meaning. Types are divided into small and large types --- sets and proper classes respectively. Each proper class, such as "group" or "topological space", has an associated notion of isomorphism in correspondence with standard definitions. Isomorphism is handled by definging a groupoid structure on the space of all definable values. The values are simultaneously objects (oids) and morphism --- they are "morphoids". Soundness can then be proved for simple and natural inference rules deriving isomorphisms and for the substitution of isomorphics.

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David McAllester. 2014-07-27. Isomorphism within Naive Type Theory. https://arxiv.org/abs/1407.7274

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