On analytic models of synthetic differential geometry
On branched covers in topos theory.
On locally simply connected toposes and their fundamental groups
On primeness and maximality of filters
On product and change of base for toposes
On the characterization of monadic categories over set
On the Grothendieck topologies in the toposes of presheaves
On the injectivity of Boolean algebras
The functor taking global elements of Boolean algebras in the topos of sheaves on a complete Boolean algebra is shown to preserve and reflect injectivity as well as completeness. This is then used to derive a result of Bell on the Boolean Ultrafilter Theorem in -valued set theory and to prove that (i) the category of complete Boolean algebras and complete homomorphisms has no non-trivial injectives, and (ii) the category of frames has no absolute retracts.
Open Maps of Toposes.
Ordered groupoids and étendues
Ordinary differential equations and their exponentials
In the context of Synthetic Differential Geometry, we discuss vector fields/ordinary differential equations as actions; in particular, we exploit function space formation (exponential spaces) in the category of actions.