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 definitions 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 k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum 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
   • CommentTimeNov 15th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexstarting article on A1-cohesive homotopy type theory, where an affine line $\mathbb{A}^1$ is used instead of $\mathbb{R}$ in real-cohesive homotopy type theory, and where the shape modality is $\mathbb{A}^1$-localization rather than $\mathbb{R}$-localization. Anonymous <a href="https://ncatlab.org/nlab/revision/A1-cohesive+homotopy+type+theory/1">v1</a>, <a href="https://ncatlab.org/nlab/show/A1-cohesive+homotopy+type+theory">current</a>

   starting article on A1-cohesive homotopy type theory, where an affine line $\mathbb{A}^1$ is used instead of $\mathbb{R}$ in real-cohesive homotopy type theory, and where the shape modality is $\mathbb{A}^1$-localization rather than $\mathbb{R}$-localization.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 16th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexIn the section on motivic HoTT ([here](https://ncatlab.org/nlab/show/A1-cohesive+homotopy+type+theory#MotivicHomotopyTypeTheory)) I have * directly linked to Mitchell's thesis * added the word "parameterized" to "stable homotopy theory" <a href="https://ncatlab.org/nlab/revision/diff/A1-cohesive+homotopy+type+theory/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/A1-cohesive+homotopy+type+theory/3">v3</a>, <a href="https://ncatlab.org/nlab/show/A1-cohesive+homotopy+type+theory">current</a>

   In the section on motivic HoTT (here) I have

   • directly linked to Mitchell’s thesis

   • added the word “parameterized” to “stable homotopy theory”

   diff, v3, current

3. • CommentRowNumber3.
   • CommentAuthornLab edit announcer
   • CommentTimeJun 22nd 2024
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexrenaming the page to "A1-homotopy type theory" and removed the stuff about cohesive homotopy type theory from the article. There is no flat modality in $\mathbb{A}_1$-homotopy theory in the sense of cohesive homotopy type theory, so any possible $\mathbb{A}_1$-homotopy type theory won't be a cohesive homotopy type theory. See the answered questions part of [https://github.com/felixwellen/synthetic-zariski/blob/main/README.md](https://github.com/felixwellen/synthetic-zariski/blob/main/README.md) Anonymouse <a href="https://ncatlab.org/nlab/revision/diff/A1-homotopy+type+theory/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/A1-homotopy+type+theory/4">v4</a>, <a href="https://ncatlab.org/nlab/show/A1-homotopy+type+theory">current</a>

   renaming the page to “A1-homotopy type theory” and removed the stuff about cohesive homotopy type theory from the article. There is no flat modality in $\mathbb{A}_1$-homotopy theory in the sense of cohesive homotopy type theory, so any possible $\mathbb{A}_1$-homotopy type theory won’t be a cohesive homotopy type theory. See the answered questions part of

   https://github.com/felixwellen/synthetic-zariski/blob/main/README.md

   Anonymouse

   diff, v4, current