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1. • CommentRowNumber1.
   • CommentAuthorMike Shulman
   • CommentTimeOct 28th 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexCreated, mainly with stuff from the overview. <a href="https://ncatlab.org/nlab/revision/Initiality+Project+-+Partial+Interpretation/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Initiality+Project+-+Partial+Interpretation">current</a>

   Created, mainly with stuff from the overview.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeOct 28th 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexAdd the clauses for variables <a href="https://ncatlab.org/nlab/revision/Initiality+Project+-+Partial+Interpretation/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Initiality+Project+-+Partial+Interpretation">current</a>

   Add the clauses for variables

   v1, current

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeOct 28th 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexAdd partial interpretation of contexts. <a href="https://ncatlab.org/nlab/revision/Initiality+Project+-+Partial+Interpretation/1">v1</a>, <a href="https://ncatlab.org/nlab/show/Initiality+Project+-+Partial+Interpretation">current</a>

   Add partial interpretation of contexts.

   v1, current

4. • CommentRowNumber4.
   • CommentAuthordlicata335
   • CommentTimeNov 1st 2018
   • PermaLink
   Author: dlicata335
   Format: MarkdownItexTo what extent is this proof of initiality intended to be constructive? I think that has some bearing on how the partial interpretations are treated. I think it should be possible to prove initiality in a constructive metalanguage, but maybe some shortcuts helpful for the intended audience are possible classically.

   To what extent is this proof of initiality intended to be constructive? I think that has some bearing on how the partial interpretations are treated. I think it should be possible to prove initiality in a constructive metalanguage, but maybe some shortcuts helpful for the intended audience are possible classically.

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeNov 1st 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI don't immediately see anything that would make it nonconstructive.

   I don’t immediately see anything that would make it nonconstructive.

6. • CommentRowNumber6.
   • CommentAuthorMike Shulman
   • CommentTimeNov 1st 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexIn particular, I think all the definitions of the partial interpretations should be expressed in purely category-theoretic language in the presheaf category $[C^{op},Set]$, which is inherently constructive, especially because the internal logic of this category is not classical. Is there something that looks nonconstructive to you?

   In particular, I think all the definitions of the partial interpretations should be expressed in purely category-theoretic language in the presheaf category , which is inherently constructive, especially because the internal logic of this category is not classical. Is there something that looks nonconstructive to you?

7. • CommentRowNumber7.
   • CommentAuthorAli Caglayan
   • CommentTimeNov 8th 2018
   • PermaLink
   Author: Ali Caglayan
   Format: MarkdownItexWhat exactly is $\Tm^{V}$ where $V$ is a finite set?

   What exactly is where is a finite set?

8. • CommentRowNumber8.
   • CommentAuthorMike Shulman
   • CommentTimeNov 8th 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThe $V$-indexed [[power]] (for $Set$-enrichment) of the presheaf $Tm$.

   The -indexed power (for -enrichment) of the presheaf .

9. • CommentRowNumber9.
   • CommentAuthorMike Shulman
   • CommentTimeNov 8th 2018
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexOtherwise known as the [[product]] of $V$ copies of $Tm$, or $\prod_{V} Tm$.

   Otherwise known as the product of copies of , or .