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1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeDec 5th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexadded definition Anonymous <a href="https://ncatlab.org/nlab/revision/diff/n-truncation+modality/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/n-truncation+modality/7">v7</a>, <a href="https://ncatlab.org/nlab/show/n-truncation+modality">current</a>

   added definition

   Anonymous

   diff, v7, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJan 4th 2023
   • (edited Jan 4th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexpolished up the previous list of references ([here](https://ncatlab.org/nlab/show/n-truncation+modality#References)) fixing a few oddities in what was there and then adding various further references such as the one by Cherubini & Rijke which the Anonymous in [#1](#Comment_105216) probably indended to add, but didn't and this one: * [[Nicolai Kraus]], *Truncation levels in Homotopy Type Theory*, Nottingham (2015) &lbrack;[pdf](https://eprints.nottingham.ac.uk/28986/1/thesis.pdf), [eprints:28986](https://eprints.nottingham.ac.uk/28986)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/n-truncation+modality/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/n-truncation+modality/8">v8</a>, <a href="https://ncatlab.org/nlab/show/n-truncation+modality">current</a>

   polished up the previous list of references (here) fixing a few oddities in what was there and then adding various further references

   such as the one by Cherubini & Rijke which the Anonymous in #1 probably indended to add, but didn’t

   and this one:

   • Nicolai Kraus, Truncation levels in Homotopy Type Theory, Nottingham (2015) [pdf, eprints:28986]

   diff, v8, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJan 4th 2023
   • (edited Jan 5th 2023)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added ([here](https://ncatlab.org/nlab/show/n-truncation+modality#ExplicitInferenceRules)) the inference rules for the $n$-truncation HIT from section 7.3 of the UFP book, together with a big diagram showing the categorical semantics. <a href="https://ncatlab.org/nlab/revision/diff/n-truncation+modality/11">diff</a>, <a href="https://ncatlab.org/nlab/revision/n-truncation+modality/11">v11</a>, <a href="https://ncatlab.org/nlab/show/n-truncation+modality">current</a>

   I have added (here) the inference rules for the $n$-truncation HIT from section 7.3 of the UFP book, together with a big diagram showing the categorical semantics.

   diff, v11, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeFeb 19th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded further mentioning that an alternative construction of $n$-truncation as an iterated [[pushout type]] is (somewhat implicit) in: * [[Egbert Rijke]], Section 7.2 (culminating in Thm. 7.2.10) of: _Classifying Types_ ([arXiv:1906.09435](https://arxiv.org/abs/1906.09435)) <a href="https://ncatlab.org/nlab/revision/diff/n-truncation+modality/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/n-truncation+modality/15">v15</a>, <a href="https://ncatlab.org/nlab/show/n-truncation+modality">current</a>

   added further mentioning that an alternative construction of $n$-truncation as an iterated pushout type is (somewhat implicit) in:

   • Egbert Rijke, Section 7.2 (culminating in Thm. 7.2.10) of: Classifying Types (arXiv:1906.09435)

   diff, v15, current