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1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeSep 2nd 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexstarting this article based upon a suggestion by Mike Shulman on the discussion thread for [[extensional type theory]], that from now on "extensional" should only be used for definitionally extensional type theories on the nLab Anonymous <a href="https://ncatlab.org/nlab/revision/set-level+type+theory/1">v1</a>, <a href="https://ncatlab.org/nlab/show/set-level+type+theory">current</a>

   starting this article based upon a suggestion by Mike Shulman on the discussion thread for extensional type theory, that from now on “extensional” should only be used for definitionally extensional type theories on the nLab

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeSep 3rd 2022
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThanks! <a href="https://ncatlab.org/nlab/revision/diff/set-level+type+theory/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/set-level+type+theory/2">v2</a>, <a href="https://ncatlab.org/nlab/show/set-level+type+theory">current</a>

   Thanks!

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeSep 3rd 2022
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexIs cubical type theory with equality reflection a thing? I mean, I suppose one could write it down, but has anyone done it?

   Is cubical type theory with equality reflection a thing? I mean, I suppose one could write it down, but has anyone done it?

4. • CommentRowNumber4.
   • CommentAuthorGuest
   • CommentTimeSep 3rd 2022
   • PermaLink
   Author: Guest
   Format: MarkdownItexThe authors of [A Cubical Language for Bishop Sets](https://arxiv.org/abs/2003.01491) briefly mentioned the possibility of adding an equality reflection rule to their cubical type theory in section 8.2 of their article.

   The authors of A Cubical Language for Bishop Sets briefly mentioned the possibility of adding an equality reflection rule to their cubical type theory in section 8.2 of their article.

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeSep 4th 2022
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexAdded list of set-level intensional type theories, taken from [[extensional type theory]]. <a href="https://ncatlab.org/nlab/revision/diff/set-level+type+theory/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/set-level+type+theory/3">v3</a>, <a href="https://ncatlab.org/nlab/show/set-level+type+theory">current</a>

   Added list of set-level intensional type theories, taken from extensional type theory.

   diff, v3, current