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David Corfield (Jan 28 2025 at 07:57):Are 'formal limit' and 'formal colimit' sufficiently precise and recognised terms to require an nLab page? They crop up here and there, such as on [[ind-pro-object]].
David Corfield (Jan 28 2025 at 08:00):For context, I was looking to understand this MO answer:
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Mike Shulman (Jan 28 2025 at 08:03):I guess the definition would be that a "formal colimit of Xs" is an object of the free cocompletion of the category of Xs under some class of colimits?
Mike Shulman (Jan 28 2025 at 08:04):Just as you might define a "formal sum" of elements of some set to be an element of the free abelian group generated by .
Mike Shulman (Jan 28 2025 at 08:05):Seems like a reasonable topic for a page to me. I wonder if there's something more general to be said about the meaning of the word "formal".
David Corfield (Jan 28 2025 at 08:10):Right, so we're seeing instances such as [[pro-object]] where the class of limit is mentioned:
A pro-object of a category is a "formal filtered limit" of objects of .
Nathanael Arkor (Jan 28 2025 at 09:20):I would be tempted just to redirect those terms to [[free cocompletion]].