B-systems and C-systems are equivalent
Benedikt Ahrens (University of Birmingham, TU Delft - Electrical Engineering, Mathematics and Computer Science)
Jacopo Emmenegger (Università degli Studi di Genova)
Paige Randall North (Universiteit Utrecht)
Egbert Rijke (University of Ljubljana)
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Abstract
C-systems were defined by Cartmell as models of generalized algebraic theories. B-systems were defined by Voevodsky in his quest to formulate and prove an initiality conjecture for type theories. They play a crucial role in Voevodsky's construction of a syntactic C-system from a term monad. In this work, we construct an equivalence between the category of C-systems and the category of B-systems, thus proving a conjecture by Voevodsky.
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