  Several different topoi have played an important role in the development and
applications of synthetic guarded domain theory (SGDT), a new kind of synthetic
domain theory that abstracts the concept of guarded recursion frequently
employed in the semantics of programming languages. In order to unify the
accounts of guarded recursion and coinduction, several authors have enriched
SGDT with multiple "clocks" parameterizing different time-streams, leading to
more complex and difficult to understand topos models. Until now these topoi
have been understood very concretely qua categories of presheaves, and the
logico-geometrical question of what theories these topoi classify has remained
open. We show that several important topos models of SGDT classify very simple
geometric theories, and that the passage to various forms of multi-clock
guarded recursion can be rephrased more compositionally in terms of the lower
bagtopos construction of Vickers and variations thereon due to Johnstone. We
contribute to the consolidation of SGDT by isolating the universal property of
multi-clock guarded recursion as a modular construction that applies to any
topos model of single-clock guarded recursion.
