Dear everyone, I have a question about terminology: What would you call a regular category in which every object has an essentially small category of quotients (the full subcategory of the coslice category consisting of regular epis)? I suppose "well-copowered"/"cowellpowered" refers to _all_ epis? -- Best regards, Ivar Rummelhoff
Ivar Rummelhoff correctly observes that "cowellpowered" connotes the (essential) smallness of the set of ALL epimorphisms with a given domain. It is reasonable to use "weakly cowellpowered" for the corresponding smallness of the set of STRONG epimorphisms; and these coincide with the regular epimorphisms in his case of a regular category. In situations more general than this, one had better explain one's meaning in unambiguous words. Max Kelly.
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Ivar Rummelhoff -
maxk＠maths.usyd.edu.au