Re: Re: monic epics

["Charles Wells" <Charles@abstractmath.org>]

It seems to me that Isbell's notion of "dominions" are something like a
precise way of saying "a complete set of generators" for the case of
epimorphisms in Cat.  Look at "Epimorphisms and Dominions III" by John
Isbell, American Journal of Mathematics, 1968.  That paper has
references to earlier papers about the case for semigroups and other
categories.

Charles Wells

> ok i got it. in all the examples given the subobjects given by the
> monics are "generators" for the object, where by "generators" i mean the
> elements of the subobject in some way determine the elements of the
> bigger object. so how about this then: any time we have the situation
> described above the monic arrow will also be epic.
>
>
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