Lemma 28.11.2. Let S be a scheme. The following are equivalent
S is catenary,
there exists an open covering of S all of whose members are catenary schemes,
for every affine open \mathop{\mathrm{Spec}}(R) = U \subset S the ring R is catenary, and
there exists an affine open covering S = \bigcup U_ i such that each U_ i is the spectrum of a catenary ring.
Moreover, in this case any locally closed subscheme of S is catenary as well.
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