# How to call a category with a single morphism between every two objects?

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?)

• A boring category? – AdLibitum Jul 9 '15 at 8:41
• 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 :) – Tac-Tics Jul 9 '15 at 8:41
• @AdLibitum, you do not call a group with a single element a boring group. – Alexey Jul 9 '15 at 8:42
• @Alexey I generally call trivial things boring. – Brian Fitzpatrick Jul 9 '15 at 8:43
• @Alexey: No. Yet it is pretty boring, isn't it? – AdLibitum Jul 9 '15 at 8:45