Infinity-Topos
An infinity-topos is an accessible left exact localization of a category of space-valued presheaves on a small infinity-category. Track both accessibility and preservation of finite limits when extending the ordinary topos analogy.
Before opening the references
Higher Categories and the Topos Bridge · Grothendieck Topos · Adjunction · Categorical Limit
Where to read
Start here: Higher Topos Theory
Jacob Lurie · Book · English · Free full text
§6.1, Definition 6.1.0.4 and Remark 6.1.0.5, printed p. 529 (accessible left exact localization and its size condition)
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Category Theory in the library · Preparation and skip guidance