All Questions
Tagged with locally-presentable-categories set-theory
4 questions
9
votes
1
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700
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Case study: what does it take to formulate and prove Quillen's small object argument in ZFC?
I'm getting a bit lost over at Peter Scholze's interesting question about removing the dependence on universes from theorems in category theory. In particular, I'm being forced to admit that I don't ...
- 64k
17
votes
2
answers
557
views
Raising the index of accessibility
In the standard reference books Locally presentable and accessible categories (Adamek-Rosicky, Theorem 2.11) and Accessible categories (Makkai-Pare, $\S$2.3), it is shown that for regular cardinals $\...
- 66.8k
7
votes
1
answer
396
views
Locally presentable categories, universes, and Vopenka's principle
Some aspects of the theory of locally presentable categories depends on set-theoretic assumptions. Namely, a large cardinal axiom known as Vopenka's principle implies several nice properties of such ...
- 4,459
10
votes
0
answers
510
views
Orthogonality relations and accessibility?
Suppose I have a pair of locally presentable categories connected by an accessible functor. Then the preimage of an accessible subcategory of the codomain is an accessible subcategory of the domain. ...
- 1,569