• Corpus ID: 235367720

Globular weak $\omega$-categories as models of a type theory

@inproceedings{Benjamin2021GlobularW,
  title={Globular weak \$\omega\$-categories as models of a type theory},
  author={Thibaut Benjamin and Eric Finster and Samuel Mimram},
  year={2021}
}
We study the dependent type theory CaTT, introduced by Finster and Mimram, which presents the theory of weak ω-categories, following the idea that type theories can be considered as presentations of generalized algebraic theories. Our main contribution is a formal proof that the models of this type theory correspond precisely to weak ω-categories, as defined by Maltsiniotis, by generalizing a definition proposed by Grothendieck for weak ωgroupoids: Those are defined as suitable presheaves over… 

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