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1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeJun 9th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexPage created, but author did not leave any comments. Anonymous <a href="https://ncatlab.org/nlab/revision/A3-space/1">v1</a>, <a href="https://ncatlab.org/nlab/show/A3-space">current</a>

   Page created, but author did not leave any comments.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeAug 30th 2022
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexWhat is the distinction being drawn here between $A_3$-spaces and $H$-monoids? Is it that an $A_3$-space has a specified associator but an $H$-monoid only has the existence of an associator? If so, that same distinction can be made in HoTT. Also, do we really need this page in addition to [[An-space]]?

   What is the distinction being drawn here between $A_3$-spaces and $H$-monoids? Is it that an $A_3$-space has a specified associator but an $H$-monoid only has the existence of an associator? If so, that same distinction can be made in HoTT.

   Also, do we really need this page in addition to An-space?

3. • CommentRowNumber3.
   • CommentAuthorGuest
   • CommentTimeAug 31st 2022
   • PermaLink
   Author: Guest
   Format: MarkdownItexiirc this page used to be on the HoTT wiki but was moved here when everything else got ported here as well.

   iirc this page used to be on the HoTT wiki but was moved here when everything else got ported here as well.

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeAug 31st 2022
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexSince most of the content on this page is in type theory, maybe we should call the page something like "$A_3$-type" and focus it explicitly on that?

   Since most of the content on this page is in type theory, maybe we should call the page something like “$A_3$-type” and focus it explicitly on that?

5. • CommentRowNumber5.
   • CommentAuthorGuest
   • CommentTimeAug 31st 2022
   • PermaLink
   Author: Guest
   Format: MarkdownItexThe nLab does something similar with higher inductive types to distinguish between a synthetic formulation in type theory and its general analytic concept (i.e. [[circle type]] vs [[circle]], [[interval type]] vs [[interval]], [[James construction type]] vs [[James construction]], [[smash product type]] vs [[smash product]], et cetera).

   The nLab does something similar with higher inductive types to distinguish between a synthetic formulation in type theory and its general analytic concept (i.e. circle type vs circle, interval type vs interval, James construction type vs James construction, smash product type vs smash product, et cetera).

6. • CommentRowNumber6.
   • CommentAuthorMike Shulman
   • CommentTimeAug 31st 2022
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexRenamed to $A_3$-type and focused on type theory. <a href="https://ncatlab.org/nlab/revision/diff/A3-type/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/A3-type/2">v2</a>, <a href="https://ncatlab.org/nlab/show/A3-type">current</a>

   Renamed to $A_3$-type and focused on type theory.

   diff, v2, current

7. • CommentRowNumber7.
   • CommentAuthorMike Shulman
   • CommentTimeAug 31st 2022
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI also just realized the definition of homomorphism of $A_3$-types was wrong! Preservation of the coherence is not by a separate function, it's by the same underlying function $\phi$. <a href="https://ncatlab.org/nlab/revision/diff/A3-type/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/A3-type/2">v2</a>, <a href="https://ncatlab.org/nlab/show/A3-type">current</a>

   I also just realized the definition of homomorphism of $A_3$-types was wrong! Preservation of the coherence is not by a separate function, it’s by the same underlying function $\phi$.

   diff, v2, current

8. • CommentRowNumber8.
   • CommentAuthornLab edit announcer
   • CommentTimeDec 19th 2023
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexThe existing literature calls these objects "associative H-spaces", i.e. * [[Ulrik Buchholtz]], [[J. Daniel Christensen]], [[Jarl G. Taxerås Flaten]], [[Egbert Rijke]], *Central H-spaces and banded types* &lbrack;[arXiv:2301.02636](https://arxiv.org/abs/2301.02636)&rbrack; so renaming page to "associative H-space" Anonymouse <a href="https://ncatlab.org/nlab/revision/diff/associative+H-space/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/associative+H-space/4">v4</a>, <a href="https://ncatlab.org/nlab/show/associative+H-space">current</a>

   The existing literature calls these objects “associative H-spaces”, i.e.

   • Ulrik Buchholtz, J. Daniel Christensen, Jarl G. Taxerås Flaten, Egbert Rijke, Central H-spaces and banded types [arXiv:2301.02636]

   so renaming page to “associative H-space”

   Anonymouse

   diff, v4, current

9. • CommentRowNumber9.
   • CommentAuthorUrs
   • CommentTimeDec 19th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexHey Anonymous(e), earlier today there was a comment on an edit of yours [here](https://nforum.ncatlab.org/discussion/15838/fundamental-theorem-of-identity-types/?Focus=114709#Comment_114709), which deserves a reaction.

   Hey Anonymous(e), earlier today there was a comment on an edit of yours here, which deserves a reaction.