Modeling Identity Types
Read OriginalThis technical article delves into the challenges of modeling identity types in dependent type theory using categorical semantics. It explains why naive models fail by equating all paths to reflexivity, and proposes a solution inspired by homotopy theory. The discussion centers on using fibrations, cofibrations, and the construction of path space objects to create a non-trivial model that supports concepts essential to homotopy type theory, such as higher inductive types and univalence.
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