相关论文: Models of Homotopy Type Theory with an Interval Ty…

We give a rather general construction of double categories and so, under further conditions, double groupoids, from a structure we call a `double module'. We also give a homotopical construction of a double groupoid from a triad consisting…

This paper contains some contributions to the study of the relationship between 2-categories and the homotopy types of their classifying spaces. Mainly, generalizations are given of both Quillen's Theorem B and Thomason's Homotopy Colimit…

Cubical type theories are designed around an abstract unit interval from which types of paths, used to represent equalities, are defined. Varying the operations available on this interval yields different type theories. A reversal is an…

In this paper we construct a cofibrantly generated model category structure on the category of all small symmetric multicategories enriched in simplicial sets.

We introduce basic notions in category theory to type theorists, including comprehension categories, categories with attributes, contextual categories, type categories, and categories with families along with additional discussions that are…

We construct a model structure on the category of ordered simplicial complexes, Quillen equivalent to the standard model structure on simplicial sets. This shows that simplicial complexes, which are fully combinatorial in nature, provide a…

Given an appropriate diagram of left Quillen functors between model categories, one can define a notion of homotopy fiber product, but one might ask if it is really the correct one. Here, we show that this homotopy pullback is well-behaved…

We introduce Displayed Type Theory (dTT), a multi-modal homotopy type theory with discrete and simplicial modes. In the intended semantics, the discrete mode is interpreted by a model for an arbitrary $\infty$-topos, while the simplicial…

We exploit the theory of $\infty$-stacks to provide some basic definitions and calculational tools regarding stratified homotopy theory of stratified topological stacks.

Simple type theory is suited as framework for combining classical and non-classical logics. This claim is based on the observation that various prominent logics, including (quantified) multimodal logics and intuitionistic logics, can be…

Homotopy type theory (HoTT) can be seen as a generalisation of structural set theory, in the sense that 0-types represent structural sets within the more general notion of types. For material set theory, we also have concrete models as…

Following a project of developing conventions and notations for informal type theory carried out in the homotopy type theory book for a framework built out of an augmentation of constructive type theory with axioms governing…

This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…

A homotopy theoretic description is given for trivial unit conjecture in the group ring ZG.

Many introductions to homotopy type theory and the univalence axiom gloss over the semantics of this new formal system in traditional set-based foundations. This expository article, written as lecture notes to accompany a 3-part mini course…

We define and develop two-level type theory (2LTT), a version of Martin-L\"of type theory which combines two different type theories. We refer to them as the inner and the outer type theory. In our case of interest, the inner theory is…

I present a short review of models for transverse-momentum distributions and transversity, with a particular attention on general features common to many models. I compare some model results with experimental extractions. I discuss the…

Given a diagram of rings, one may consider the category of modules over them. We are interested in the homotopy theory of categories of this type: given a suitable diagram of model categories M(s) (as s runs through the diagram), we…

We introduce the notion of (half) 2-adjoint equivalences in Homotopy Type Theory and prove their expected properties. We formalized these results in the Lean Theorem Prover.

A general framework of latent trait item response models for continuous responses is given. In contrast to classical test theory models, which traditionally distinguish between true scores and error scores, the responses are clearly linked…