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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 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 nonassociative 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.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 17th 2018
   • (edited Oct 17th 2018)
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThere's [discussion](https://golem.ph.utexas.edu/category/2018/10/topoi_of_gsets.html) about 'atomic' matters at the Café at the moment. Another thicket of naming conventions, it would seem. Would I be right in thinking there is no connection between the clusters: * [[atomic category]], [[tiny object]], [[atom]] and * [[atomic topos]], [[atomic geometric morphism]], [[atomic site]]? Then there's Barwick's [atomic ∞-category](https://ncatlab.org/nlab/show/Parametrized+Higher+Category+Theory+and+Higher+Algebra) which is different again.

   There’s discussion about ’atomic’ matters at the Café at the moment. Another thicket of naming conventions, it would seem. Would I be right in thinking there is no connection between the clusters:

   • atomic category, tiny object, atom

   and

   • atomic topos, atomic geometric morphism, atomic site?

   Then there’s Barwick’s atomic ∞-category which is different again.

2. • CommentRowNumber2.
   • CommentAuthorAli Caglayan
   • CommentTimeOct 17th 2018
   • PermaLink
   Author: Ali Caglayan
   Format: MarkdownItexDavid, your first "discussion" link is missing the l at the end.

   David, your first “discussion” link is missing the l at the end.

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 17th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThanks. Fixed.

   Thanks. Fixed.

4. • CommentRowNumber4.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 17th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexOh they do connect. At [[atomic topos]] it says > Definition 2.2. A non-zero object $A$ of a topos $\mathcal{E}$ is an [[atom]] if its only subobjects are $A$ and $0$, and that a topos being atomic is the same as having a small generating set of atoms.

   Oh they do connect. At atomic topos it says

   Definition 2.2. A non-zero object $A$ of a topos $\mathcal{E}$ is an atom if its only subobjects are $A$ and $0$,

   and that a topos being atomic is the same as having a small generating set of atoms.

5. • CommentRowNumber5.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 17th 2018
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexThis at [Indecomposability vs irreducibility](https://ncatlab.org/nlab/show/indecomposable+object#irreducible) adds to the fun: >The bottom line is that ‘irreducible’ and ‘indecomposable’ sometimes mean the same thing but sometimes don't, and ‘irreducible’ doesn't even mean the same thing across different fields. So we have simple, atomic, indecomposable and irreducible to worry about.

   This at Indecomposability vs irreducibility adds to the fun:

   The bottom line is that ‘irreducible’ and ‘indecomposable’ sometimes mean the same thing but sometimes don’t, and ‘irreducible’ doesn’t even mean the same thing across different fields.

   So we have simple, atomic, indecomposable and irreducible to worry about.