Add property: ℵ₁-filtered colimits (WIP)#179
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@ykawase5048 Can you perhaps help here? |
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TBA
This PR adds two properties:
As for ℵ₁-filtered, all categories have been decided. As for ℵ₁-filtered colimits, the following need to be decided, most of which look doable (except for FreeAb ...). At this point, I should also try to decide ℵ₁-accessible, which is open for several categories. Probably there is a general lemma which is similar to the Theorem 2.2.2 in Makkai-Paré.
I think the following is true: a cauchy complete countable locally finite category is ℵ₁-accessible.
TODO: prove that theorem (WIP)
category of finite sets and injections -- will follow from the theorem
category of free abelian groups -- (skip this)
category of metric spaces with continuous maps
category of schemes -- (skip this)
delooping of the additive monoid of natural numbers
delooping of the additive monoid of ordinal numbers