Grothendieck Topos
A Grothendieck topos collects the sheaves on a site into a geometric setting in its own right. Read the definition together with morphisms of topoi and the punctual example to see how the sheaf category carries more flexible maps than a chosen site presentation.
Before opening the references
Where to read
Start here: The Stacks Project — Topoi
The Stacks Project Authors · Online reference · English · Free full text
Section 7.15, Definition 7.15.1 and the following discussion of the punctual topos
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Algebraic Geometry in the library · Preparation and skip guidance