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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