I would suggest "cancellative categories" - I believe the corresponding term "cancellative monoid" is standard. Steve Lack. On 5/02/10 4:39 AM, "lamarche" <lamarche@loria.fr> wrote:

Is there a standard accepted name for categories all whose morphisms are both epi and mono? This includes groupoids, posets and preorders, along with free categories (from graphs), so it's not a trivial class at all.

I am leaning towards calling them "integral categories", by analogy with integral domains, but Google searches have been frustrating. Another possiblility would be "cancellation categories" (they have both the left and right cancellation property), but I'm not sure I like this one.

Is there anything about these in the literature already?

Thanks in advance,

François

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