B-SYSTEMS AND C-SYSTEMS ARE EQUIVALENT

Author:

AHRENS BENEDIKTORCID,EMMENEGGER JACOPOORCID,NORTH PAIGE RANDALLORCID,RIJKE EGBERTORCID

Abstract

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.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference15 articles.

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5. [1] Ahrens, B. , Emmenegger, J. , North, P. R. , and Rijke, E. , Algebraic presentations of dependent type theories, submitted, 2022, preprint available at arXiv:2111.09948v2.

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