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Mar 21 at 13:18 vote accept Jochen Wengenroth
Mar 20 at 15:11 comment added Jochen Wengenroth Of course, isometries and similarities are also yield important categrories (but they do not seem to have interesting quotients).
Mar 19 at 19:39 comment added Michael Hardy Suppose $(X, d)$ is a metric space and $f:X\to X$ and for all $x,y\in X,$ $d(f(x),f(y)) \le d(x,y)$ and the image of $f$ is pointwise fixed under $f.$ Could that image be considered a sort of quotient of $X \text{?}$
Mar 19 at 19:18 comment added Michael Hardy Would you also include isometries and similarities among "natural choices of morphisms"?
Mar 19 at 19:15 history edited Michael Hardy CC BY-SA 4.0
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Mar 19 at 19:05 answer added Tyrone timeline score: 2
Mar 19 at 14:13 comment added Jochen Wengenroth @Tyrone Thanks for correcting my typos.
Mar 19 at 9:07 history edited Tyrone CC BY-SA 4.0
Several minor typos.
Mar 18 at 13:45 history asked Jochen Wengenroth CC BY-SA 4.0