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2$\begingroup$ The constructions in everyday's combinatorial model categories (e.g. the cofibrant or fibrant replacement functors) are "small" in the sense that they depend on a transfinite cardinal like $\aleph_0$, $\aleph_1$ or $\aleph_2$. The cardinals $\aleph_0$, $\aleph_1$ or $\aleph_2$ do not change with a change of universe. $\endgroup$Philippe Gaucher– Philippe Gaucher2017-08-25 11:43:09 +00:00Commented Aug 25, 2017 at 11:43
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