The Strict ω-Groupoid Interpretation of Type Theory
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چکیده
Hofmann and Streicher showed that there is a model of the intensional form of Martin-Löf’s type theory obtained by interpreting closed types as groupoids. We show that there is also a model when closed types are interpreted as strict ω-groupoids. The nonderivability of various truncation and uniqueness principles in intensional type theory is then an immediate consequence. In the process of constructing the interpretation we develop some ω-categorical machinery including a version of the Grothendieck construction for strict ω-categories.
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تاریخ انتشار 2011