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2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

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!

6. • CommentRowNumber6.
   • CommentAuthorJohn Baez
   • CommentTimeJun 20th 2024
   • PermaLink
   Author: John Baez
   Format: MarkdownItexAt the start of this article, should > An object e of E is called tiny, small-projective object be > An object e of E is called a tiny, or small-projective object ? If so, could someone please change it?

   At the start of this article, should

   An object e of E is called tiny, small-projective object

   be

   An object e of E is called a tiny, or small-projective object

   ? If so, could someone please change it?

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeJun 21st 2024
   • (edited Jun 21st 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexHave fixed this, together with a couple of other little issues. <a href="https://ncatlab.org/nlab/revision/diff/tiny+object/43">diff</a>, <a href="https://ncatlab.org/nlab/revision/tiny+object/43">v43</a>, <a href="https://ncatlab.org/nlab/show/tiny+object">current</a>

   Have fixed this, together with a couple of other little issues.

   diff, v43, current