Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeJun 9th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexcopying reference from HoTT wiki Anonymous <a href="https://ncatlab.org/nlab/revision/Modalities+in+homotopy+type+theory/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Modalities+in+homotopy+type+theory">current</a>

   copying reference from HoTT wiki

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 9th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexIn adding the missing publication data, I have taken the liberty of (hyperlinking the abstract and) re-formatting as follows -- what do you think: *** * [[Egbert Rijke]], [[Michael Shulman]], [[Bas Spitters]]: **Modalities in homotopy type theory** Logical Methods in Computer Science **16** 1 (2020) [arXiv:1706.07526](https://arxiv.org/abs/1706.07526) <a href="https://doi.org/10.23638/LMCS-16(1:2)2020">lmcs:3826</a> on [[modal homotopy type theory]]. > **Abstract.** [[univalence|Univalent]] [[homotopy type theory]] (HoTT) may be seen as a language for the [[(infinity,1)-category|category]] of [[infinity-groupoid|$\infty$-groupoids]]. It is being developed as a [[univalent foundations|new foundation for mathematics]] and as an [[internal language]] for ([[elementary (infinity,1)-topos|elementary]]) [[(infinity,1)-topos|higher toposes]]. We develop the theory of [[factorization systems]], [[reflective subuniverses]], and [[modalities]] in [[homotopy type theory]], including their construction using a "[[localization]]" [[higher inductive type]]. This produces in particular the [[(n-connected, n-truncated) factorization system|($n$-connected, $n$-truncated) factorization system]] as well as internal presentations of [[subtoposes]], through [[lex]] [[modalities]]. We also develop the [[categorical semantics|semantics]] of these constructions. *** <a href="https://ncatlab.org/nlab/revision/diff/Modalities+in+homotopy+type+theory/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/Modalities+in+homotopy+type+theory/2">v2</a>, <a href="https://ncatlab.org/nlab/show/Modalities+in+homotopy+type+theory">current</a>

   In adding the missing publication data, I have taken the liberty of (hyperlinking the abstract and) re-formatting as follows – what do you think:

   ---

   • Egbert Rijke, Michael Shulman, Bas Spitters:

     Modalities in homotopy type theory

     Logical Methods in Computer Science 16 1 (2020)

     arXiv:1706.07526

     lmcs:3826

   on modal homotopy type theory.

   Abstract. Univalent homotopy type theory (HoTT) may be seen as a language for the category of $\infty$-groupoids. It is being developed as a new foundation for mathematics and as an internal language for (elementary) higher toposes. We develop the theory of factorization systems, reflective subuniverses, and modalities in homotopy type theory, including their construction using a “localization” higher inductive type. This produces in particular the ($n$-connected, $n$-truncated) factorization system as well as internal presentations of subtoposes, through lex modalities. We also develop the semantics of these constructions.

   ---

   diff, v2, current