Stable factorization from a fibred algebraic weak factorization system

10/07/2019

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by   Evan Cavallo, et al.

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We present a construction of stable diagonal factorizations, used to define categorical models of type theory with identity types, from a family of algebraic weak factorization systems on the slices of a category. Inspired by a computational interpretation of indexed inductive types in cubical type theory due to Cavallo and Harper, it can be read as a refactoring of a construction of van den Berg and Garner, and is a new alternative among a variety of approaches to modeling identity types in the literature.