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    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeJan 11th 2011
    • (edited Jan 11th 2011)

    New entry thread needed at newly expanded pro-object. Adequate changes at filtered limit.

    While threads are elements in the cofiltered limit of sets or spaces, germs are classes of equivalence which appear in the treatment of filtered colimits. However the entry germ is taking germs just in the special case of colimits forming stalks of an etale space. In my practice the notion of germ could be used more generally for directed colimits or even filtered colimits in groups, sets, and alike. Is it only me using the terminology in this extended sense ? I would like to know the opinions.

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeJan 11th 2011
    • (edited Jan 12th 2011)

    There is the notion of a germ of a map between spaces (cf microbundles)

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeJan 12th 2011

    I’ve never heard of “germ” used in the extremely general sense of “element of a filtered colimit,” but I don’t think it would bother me.

    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeJan 12th 2011

    I would certainly want the familiar specialised senses of ‘germ’ to appear, as they do, but no problem with giving the more general meanings too.