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    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 17th 2018
    • (edited Oct 17th 2018)

    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:

    and

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

    • CommentRowNumber2.
    • CommentAuthorAli Caglayan
    • CommentTimeOct 17th 2018

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

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 17th 2018

    Thanks. Fixed.

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 17th 2018

    Oh they do connect. At atomic topos it says

    Definition 2.2. A non-zero object AA of a topos \mathcal{E} is an atom if its only subobjects are AA and 00,

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

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 17th 2018

    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.