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Jun 15, 2012 at 21:49 comment added Benjamin Steinberg I meant the composition of partial functions is defined on those points of X for which it makese sense.
Jun 15, 2012 at 21:47 comment added Salvo Tringali Then, as for your case, the composition of two partial functions (from $X$ to $X$) makes always sense. Thanks for the clarification
Jun 15, 2012 at 21:07 comment added Benjamin Steinberg I mean composition as binary relations.
Jun 15, 2012 at 20:08 comment added Salvo Tringali Thank you, Benjamin. But I'm not quite sure to understand what you mean by saying that the composition of partial functions (from $X$ to itself) could make no sense in some cases. Partial functions (between sets) should be composed with each other in the same way as binary relations. Then, the corresponding category would be equivalent to the usual category of pointed sets.
Jun 15, 2012 at 15:39 history edited Benjamin Steinberg CC BY-SA 3.0
added 44 characters in body; added 3 characters in body; added 4 characters in body
Jun 15, 2012 at 15:33 history answered Benjamin Steinberg CC BY-SA 3.0