The Stacks project

59.2 Which sections to skip on a first reading?

We want to use the material in this chapter for the development of theory related to algebraic spaces, Deligne-Mumford stacks, algebraic stacks, etc. Thus we have added some pretty technical material to the original exposition of étale cohomology for schemes. The reader can recognize this material by the frequency of the word “topos”, or by discussions related to set theory, or by proofs dealing with very general properties of morphisms of schemes. Some of these discussions can be skipped on a first reading.

In particular, we suggest that the reader skip the following sections:

  1. Comparing big and small topoi, Section 59.99.

  2. Recovering morphisms, Section 59.40.

  3. Push and pull, Section 59.41.

  4. Property (A), Section 59.42.

  5. Property (B), Section 59.43.

  6. Property (C), Section 59.44.

  7. Topological invariance of the small étale site, Section 59.45.

  8. Integral universally injective morphisms, Section 59.47.

  9. Big sites and pushforward, Section 59.48.

  10. Exactness of big lower shriek, Section 59.49.

Besides these sections there are some sporadic results that may be skipped that the reader can recognize by the keywords given above.

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