Jesus: if you want more on (slightly) higher categories, try these papers by students of mine. That's what we're mainly working on these days! I have carefully edited all these papers:

* Kenny Courser, A bicategory
of decorated cospans
, Theory and Applications of Categories 32
(2017), 985–1027. (Blog article here.)

* Daniel Cicala, Spans of
cospans
.

* Daniel Cicala and Kenny Courser, Spans and cospans in a topos.

* John Baez and Kenny Courser, Coarse-graining open Markov processes. (Blog article here.)

* John Baez and Jade Master,
Open Petri nets.
(Blog articles here.)

All these papers are related. We're coming out with a lot more in a while!