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Indexed type theories
Mathematical Structures in Computer Science ( IF 0.592 ) Pub Date : 2020-05-22 , DOI: 10.1017/s0960129520000092
Valery Isaev

In this paper, we define indexed type theories which are related to indexed (∞-)categories in the same way as (homotopy) type theories are related to (∞-)categories. We define several standard constructions for such theories including finite (co)limits, arbitrary (co)products, exponents, object classifiers, and orthogonal factorization systems. We also prove that these constructions are equivalent to their type theoretic counterparts such as Σ-types, unit types, identity types, finite higher inductive types, Π-types, univalent universes, and higher modalities.
更新日期:2020-05-22

 

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