Spahn
Lawvere-Tierney operator
The closure operator
Definition
A Lawvere–Tierney topology in is (internally) a closure operator given by a left exact idempotent monad on the internal meet-semilattice .
This means that: a Lawvere–Tierney topology in is a morphism
such that
-
, equivalently (‘if is true, then is locally true’)
-
(‘ is locally locally true iff is locally true’);
-
(‘ is locally true iff and are each locally true’)
Here is the internal partial order on , and is the internal meet.
This appears for instance as (MacLaneMoerdijk, V 1.).