  Our aim in this work is to provide an explicit, simple construction of
pull-push of local systems as a lax monoidal functor. To this end, we show that
one can solve horn filling problems Cat_\infty using left Kan extensions, and
use this to provide an explicit construction of a left Kan extension functor.
We use this result to show that pull-push of local systems induces a functor
from Span(S), the infinity category of spans of spaces, into Cat_\infty. We
then develop a machinery of monoidal Beck-Chevalley fibrations, and use this to
show that the pull-push functor above admits a lax monoidal structure.
