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Hm, it’s not clear that non-standard terminology for a trivial idea needs two separate pages, particularly if neither has anything interesting to say, so far.
At least the entries should give references for where notation is used this way, if it is. I’d rather expect that if “Inj” is used for any category in the literature, then for subcategories of injective objects, but of course I haven’t made a survey.
My attention was drawn to this by someone on Twitter asking for a name for the category, and finding Inj already here
Let’s see, it’s there on p.720 of
But others use it for the category whose objects are injective set functions.
Whatever we do, Inj is a page called by other pages, such as power set.
Should that be commutative semigroup rather than commutative monoid? The unit structure $$I \to M$$ shouldn’t be there if we’re discussing surjections.
Added web source to
Was it necessary to delete the reference
Maybe put it back in with a note that he heavily uses $FinSurj$ (which he calls $Surj$) in it.
I removed it because Paré’s paper had an incorrect assertion about the characterisation of $FinSurj$. Maybe it could be added back in with a remark, though.
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