How to call a category where for every pair of objects $A, B$, there is a unique morphism $f\colon A\to B$? (A trivial category?)

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    $\begingroup$ A boring category? $\endgroup$ – AdLibitum Jul 9 '15 at 8:41
  • $\begingroup$ I wouldn't know if there's an official name, but it is defined analogously to a complete graph. However, "complete category" means something different :) $\endgroup$ – Tac-Tics Jul 9 '15 at 8:41
  • $\begingroup$ @AdLibitum, you do not call a group with a single element a boring group. $\endgroup$ – Alexey Jul 9 '15 at 8:42
  • $\begingroup$ @Alexey I generally call trivial things boring. $\endgroup$ – Brian Fitzpatrick Jul 9 '15 at 8:43
  • $\begingroup$ @Alexey: No. Yet it is pretty boring, isn't it? $\endgroup$ – AdLibitum Jul 9 '15 at 8:45

These categories are called indiscrete.

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    $\begingroup$ Of course, "indiscrete" started off as a pun on "indiscreet". Some argue that it's a bad pun and that we should say "codiscrete" instead. E.g. here. $\endgroup$ – tcamps Jul 15 '15 at 18:06

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