The Stacks project

113.11 Lisse étale site of an algebraic stack

This has been introduced in Cohomology of Stacks, Section 103.14. An example to show that it is not functorial with respect to $1$-morphisms of algebraic stacks is discussed in Examples, Section 110.59. Of course a lot more could be said about this, but it turns out to be very useful to prove things using the “big” étale site as much as possible.

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