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1. • CommentRowNumber1.
   • CommentAuthorvarkor
   • CommentTimeApr 4th 2023
   • PermaLink
   Author: varkor
   Format: MarkdownItexAdd terminology "absolutely presentable". <a href="https://ncatlab.org/nlab/revision/diff/tiny+object/40">diff</a>, <a href="https://ncatlab.org/nlab/revision/tiny+object/40">v40</a>, <a href="https://ncatlab.org/nlab/show/tiny+object">current</a>

   Add terminology “absolutely presentable”.

   diff, v40, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 5th 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Mitchell Riley]], *A Type Theory with a Tiny Object* &lbrack;[arXiv:2403.01939](https://arxiv.org/abs/2403.01939)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/tiny+object/41">diff</a>, <a href="https://ncatlab.org/nlab/revision/tiny+object/41">v41</a>, <a href="https://ncatlab.org/nlab/show/tiny+object">current</a>

   added pointer to:

   • Mitchell Riley, A Type Theory with a Tiny Object [arXiv:2403.01939]

   diff, v41, current

3. • CommentRowNumber3.
   • CommentAuthormaxsnew
   • CommentTimeMar 5th 2024
   • PermaLink
   Author: maxsnew
   Format: MarkdownItexIn this paper, Mitchell says that representable presheaves are tiny when the base category C has finite products, but the nlab page says that this is true with no assumptions about the base category. I don't see any dependence on finite products in the construction, am I missing something? Maybe he is just confusing this with the fact that powering by a representable has a simpler formulation when the base category has cartesian products.

   In this paper, Mitchell says that representable presheaves are tiny when the base category C has finite products, but the nlab page says that this is true with no assumptions about the base category. I don’t see any dependence on finite products in the construction, am I missing something? Maybe he is just confusing this with the fact that powering by a representable has a simpler formulation when the base category has cartesian products.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMar 5th 2024
   • (edited Mar 5th 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexLet's see. I suppose this is because Mitchell requires the *internal* hom out of a tiny object to preserve colimits (p. 1). A sufficient condition for reducing this requirement, in the case of representable presheaves, to the argument given on the nLab page for the *external* hom is that the site has finite products.

   Let’s see. I suppose this is because Mitchell requires the internal hom out of a tiny object to preserve colimits (p. 1).

   A sufficient condition for reducing this requirement, in the case of representable presheaves, to the argument given on the nLab page for the external hom is that the site has finite products.

5. • CommentRowNumber5.
   • CommentAuthormaxsnew
   • CommentTimeMar 5th 2024
   • PermaLink
   Author: maxsnew
   Format: MarkdownItexOh and I see now that this is mentioned already on the page (2.4). Carry on!

   Oh and I see now that this is mentioned already on the page (2.4). Carry on!