# Categorical structures for type theory in univalent foundations

@article{Ahrens2018CategoricalSF, title={Categorical structures for type theory in univalent foundations}, author={B. Ahrens and P. Lumsdaine and V. Voevodsky}, journal={ArXiv}, year={2018}, volume={abs/1705.04310} }

In this paper, we analyze and compare three of the many algebraic structures
that have been used for modeling dependent type theories: categories with
families, split type-categories, and representable maps of presheaves. We study
these in univalent type theory, where the comparisons between them can be given
more elementarily than in set-theoretic foundations. Specifically, we construct
maps between the various types of structures, and show that assuming the
Univalence axiom, some of the… CONTINUE READING

#### Topics from this paper.

7 Citations

Categories with Families: Unityped, Simply Typed, and Dependently Typed

- Mathematics, Computer Science
- 2019

2

Internal $\infty$-Categorical Models of Dependent Type Theory: Towards 2LTT Eating HoTT

- Computer Science, Mathematics
- 2020

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 27 REFERENCES

An experimental library of formalized Mathematics based on the univalent foundations

- Computer Science, Mathematics
- 2015

52