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.
category of finite sets and injections
category of free abelian groups
category of metric spaces with continuous maps
category of schemes
delooping of the additive monoid of natural numbers
delooping of the additive monoid of ordinal numbers