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forcing, large cardinals, descriptive set theory, infinite combinatorics, cardinal characteristics, forcing axioms, ultrapowers, measures, reflection, pcf theory, models of set theory, axioms of set theory, independence, axiom of choice, continuum hypothesis, determinacy, Borel equivalence relations, Boolean-valued models, embeddings, orders, relations, transfinite recursion, set theory as a foundation of mathematics, the philosophy of set theory.
6
votes
What's an example of a locally presentable category "in nature" that's not $\aleph_0$-locall...
The category of $\Delta$-generated spaces (the full category of the category of general topological spaces which are colimits of simplices) is locally $\lambda$-presentable for a regular cardinal $\la …
1
vote
On the foundations for large categories
This should be a comment, not an answer but it is too long ! This issue is not open. On the contrary, it is well-known. Unlike what is commonly believed, ZFC alone is not sufficient to develop categor …