The Stacks project

Remark 63.4.2. Of the properties of morphisms which are stable under base change (as listed in Remark 63.4.1) the following are also stable under compositions:

  1. closed, open and locally closed immersions, see Schemes, Lemma 26.24.3,

  2. quasi-compact, see Schemes, Lemma 26.19.4,

  3. universally closed, see Morphisms, Lemma 29.41.4,

  4. (quasi-)separated, see Schemes, Lemma 26.21.12,

  5. monomorphism, see Schemes, Lemma 26.23.4,

  6. surjective, see Morphisms, Lemma 29.9.2,

  7. universally injective, see Morphisms, Lemma 29.10.5,

  8. affine, see Morphisms, Lemma 29.11.7,

  9. quasi-affine, see Morphisms, Lemma 29.13.4,

  10. (locally) of finite type, see Morphisms, Lemma 29.15.3,

  11. (locally) quasi-finite, see Morphisms, Lemma 29.20.12,

  12. (locally) of finite presentation, see Morphisms, Lemma 29.21.3,

  13. universally open, see Morphisms, Lemma 29.23.3,

  14. flat, see Morphisms, Lemma 29.25.6,

  15. syntomic, see Morphisms, Lemma 29.30.3,

  16. smooth, see Morphisms, Lemma 29.34.4,

  17. unramified (resp. G-unramified), see Morphisms, Lemma 29.35.4,

  18. ├ętale, see Morphisms, Lemma 29.36.3,

  19. proper, see Morphisms, Lemma 29.41.4,

  20. H-projective, see Morphisms, Lemma 29.43.7,

  21. finite or integral, see Morphisms, Lemma 29.44.5,

  22. finite locally free, see Morphisms, Lemma 29.48.3,

  23. universally submersive, see Morphisms, Lemma 29.24.3,

  24. universal homeomorphism, see Morphisms, Lemma 29.45.3.

Add more as needed.


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