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• CommentRowNumber1.
• CommentAuthorTodd_Trimble
• CommentTimeNov 26th 2011

Added a new Properties section to connected object. Including a theorem which is a bit of a hack (where I leave it to others to decide if ’hack’ should be interpreted positively or negatively!).

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 28th 2011

Thanks. Do we have something to point to for “$\infty$-extensitivity”?

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeOct 13th 2021

In the proof here that in extensive categories connected objects are primitive with respect to coproducts, I have added cross-pointers to the properties of extensive categories that are being used.

Also I adjusted the wording of the proof a little, for streamlining.

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeNov 7th 2021
• (edited Nov 7th 2021)

Re-reading this proof (here) that in extensive categories connected objects are equivalently the indecomposables, I didn’t see how its first part proved what it claimed to be proving (I didn’t write this, originally). So I have now expanded/rewritten that first part, adding a tikzcd-diagram which shows what, I think, the actual argument is.

• CommentRowNumber5.
• CommentAuthorUrs
• CommentTimeNov 7th 2021
• (edited Nov 7th 2021)

In the old remark (here) that the initial object is not connected, I have made explicit why not.

In fact, it used to say, without explanation: “except in degenerate cases”. I have removed this claus, since it’s clearly true in general.