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Stream: learning: questions

Topic: formal limit/colimit


view this post on Zulip 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]].

view this post on Zulip David Corfield (Jan 28 2025 at 08:00):

For context, I was looking to understand this MO answer:
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view this post on Zulip 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?

view this post on Zulip Mike Shulman (Jan 28 2025 at 08:04):

Just as you might define a "formal sum" of elements of some set XX to be an element of the free abelian group generated by XX.

view this post on Zulip 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".

view this post on Zulip 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 CC is a "formal filtered limit" of objects of CC.

view this post on Zulip Nathanael Arkor (Jan 28 2025 at 09:20):

I would be tempted just to redirect those terms to [[free cocompletion]].