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