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Stream: learning: questions

Topic: regularly well powered?

Paolo Perrone (Dec 07 2021 at 23:12):

A category is called well powered if the subobjects of any given object form a (small) set.
Is there a standard name for a category where the regular subobjects form a set?

Zhen Lin Low (Dec 07 2021 at 23:15):

I believe that, yes, "regularly wellpowered" means that.

Mike Shulman (Dec 07 2021 at 23:42):

...which has the unfortunate consequence that a category in which the strong subobjects form a set is called "strongly wellpowered", that being a weaker condition than ordinary wellpoweredness...

Fawzi Hreiki (Dec 08 2021 at 13:14):

Where does the term ‘well-powered’ come from to begin with?

Zhen Lin Low (Dec 08 2021 at 13:16):

"Power" here surely refers to the powerset...

Fawzi Hreiki (Dec 08 2021 at 13:30):

I presumed so, although I guess ‘small powered’ would have been more clear.

Zhen Lin Low (Dec 08 2021 at 13:31):

That, to me, sounds more to do with powers-as-in-cotensors.