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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 definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite 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 k-theory lie-theory limits linear linear-algebra locale localization logic mathematics 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 3rd 2025
   • PermaLink
   Author: varkor
   Format: MarkdownItexAdded a reference for the main theorem. <a href="https://ncatlab.org/nlab/revision/diff/atomic+category/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/atomic+category/3">v3</a>, <a href="https://ncatlab.org/nlab/show/atomic+category">current</a>

   Added a reference for the main theorem.

   diff, v3, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeApr 3rd 2025
   • (edited Apr 3rd 2025)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded links: * Claudia Centazzo, [[Jiří Rosický]], [[Enrico M. Vitale]]: *A characterization of locally $D$-presentable categories*, [[Cahiers]] de topologie et géométrie différentielle catégoriques **45** 2 (2004) 141-146 &lbrack;[numdam:CTGDC_2004__45_2_141_0](https://www.numdam.org/item/CTGDC_2004__45_2_141_0), [pdf](https://perso.uclouvain.be/enrico.vitale/ClaudiaJiri.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/atomic+category/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/atomic+category/4">v4</a>, <a href="https://ncatlab.org/nlab/show/atomic+category">current</a>

   added links:

   • Claudia Centazzo, Jiří Rosický, Enrico M. Vitale: A characterization of locally -presentable categories, Cahiers de topologie et géométrie différentielle catégoriques 45 2 (2004) 141-146 [numdam:CTGDC_2004__45_2_141_0, pdf]

   diff, v4, current

3. • CommentRowNumber3.
   • CommentAuthorJohn Baez
   • CommentTimeApr 3rd 2025
   • PermaLink
   Author: John Baez
   Format: MarkdownItexCleaned up theorem statement and added explicit link to the paper proving this theorem. <a href="https://ncatlab.org/nlab/revision/diff/atomic+category/5">diff</a>, <a href="https://ncatlab.org/nlab/revision/atomic+category/5">v5</a>, <a href="https://ncatlab.org/nlab/show/atomic+category">current</a>

   Cleaned up theorem statement and added explicit link to the paper proving this theorem.

   diff, v5, current

4. • CommentRowNumber4.
   • CommentAuthorJohn Baez
   • CommentTimeApr 3rd 2025
   • PermaLink
   Author: John Baez
   Format: MarkdownItexClarified definition of "atomic object" as used in the definition of "atomic category". This seems wise since the formerly present link to [[atomic object]] redirected to [[tiny object]], which warns the reader that the term "atomic object" is used in a number of senses. <a href="https://ncatlab.org/nlab/revision/diff/atomic+category/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/atomic+category/7">v7</a>, <a href="https://ncatlab.org/nlab/show/atomic+category">current</a>

   Clarified definition of “atomic object” as used in the definition of “atomic category”. This seems wise since the formerly present link to atomic object redirected to tiny object, which warns the reader that the term “atomic object” is used in a number of senses.

   diff, v7, current