I have expanded the wording to avoid the impression that all three of the articles referenced use that terminology.

Also added more hyperlinks to author names and web resources.

]]>Added an earlier reference.

]]>Add an early reference.

]]>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.

]]>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.

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.

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

]]>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!).

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