locally ringed topos
Cohomology and homotopy
In higher category theory
A locally ringed topos is a locally algebra-ed topos for the theory of local rings.
This is a special case of the following equivalent definitions:
A locally ringed topos is a topos equipped with a commutative ring object (see ringed topos) that in addition satisfies the axioms
(note these are axioms for a geometric theory, interpreted according to Kripke-Joyal semantics in a topos).
Definition 1 is indeed a special case of def. 3.
This is for instance in (Johnstone) and in (Lurie, remark 2.5.11)
Section VIII.6 of
Section abc of
Section 2.5 of
Section 14.33 of
Revised on January 23, 2012 14:28:54
by Todd Trimble