Remark 57.4.1. Here is a list of properties/types of morphisms which are *stable under arbitrary base change*:

closed, open, and locally closed immersions, see Schemes, Lemma 25.18.2,

quasi-compact, see Schemes, Lemma 25.19.3,

universally closed, see Schemes, Definition 25.20.1,

(quasi-)separated, see Schemes, Lemma 25.21.13,

monomorphism, see Schemes, Lemma 25.23.5

surjective, see Morphisms, Lemma 28.9.4,

universally injective, see Morphisms, Lemma 28.10.2,

affine, see Morphisms, Lemma 28.11.8,

quasi-affine, see Morphisms, Lemma 28.12.5,

(locally) of finite type, see Morphisms, Lemma 28.14.4,

(locally) quasi-finite, see Morphisms, Lemma 28.19.13,

(locally) of finite presentation, see Morphisms, Lemma 28.20.4,

locally of finite type of relative dimension $d$, see Morphisms, Lemma 28.28.2,

universally open, see Morphisms, Definition 28.22.1,

flat, see Morphisms, Lemma 28.24.7,

syntomic, see Morphisms, Lemma 28.29.4,

smooth, see Morphisms, Lemma 28.32.5,

unramified (resp. G-unramified), see Morphisms, Lemma 28.33.5,

étale, see Morphisms, Lemma 28.34.4,

proper, see Morphisms, Lemma 28.39.5,

H-projective, see Morphisms, Lemma 28.41.8,

(locally) projective, see Morphisms, Lemma 28.41.9,

finite or integral, see Morphisms, Lemma 28.42.6,

finite locally free, see Morphisms, Lemma 28.46.4,

universally submersive, see Morphisms, Lemma 28.23.2,

universal homeomorphism, see Morphisms, Lemma 28.43.2.

Add more as needed.

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