Cohomology and homotopy
In higher category theory
Let be a topos, regarded as a base topos.
An -indexed topos is an -indexed category such that
for each object the fiber is a topos;
for each morphism in the corresponding transition functor is a logical morphism.
An -indexed geometric morphism is an -indexed adjunction between -indexed toposes, such that is left exact.
This yields a 2-category of -indexed toposes.
This appears at (Johnstone, p. 369).
- For a geometric morphism, the induced morphism (discussed at base topos) is an -indexed topos.
Write Topos for the slice 2-category of toposes over . This is a full sub-2-category -indexed toposes
This appears as (Johnstone, prop. 3.1.3).
Section B3.1 of
Revised on August 30, 2013 11:29:33
by David Corfield