Combining transition systems can be easily achieved with limits, subobjects and fibrations. However, applying this dogma to stochastic systems leads to several hurdles. In fact, the suitable notion of morphism between probability spaces fails to be closed under composition, and hence, we obtain a non-category! After covering the notions of weak categories in the iterature, we end up with Freyd's framework on paracategories. Then, we recover the notion of limit and fibration via adjunctions. This is achieved in two different ways, both capitalizing on the cartesian closed category of paracategories. On one hand, we generalize Lawvere's comma construction and define adjunction through isomorphism. On the other hand, based on the monoid classifier \Delta, we internalize paracategories, and then consider the notion of enriched-adjunction which ensues. The latter reformulation can be interpreted in any category which admits the construction of a bicategory of partial maps. We conclude by applying the established results to the fibred paracategories of stochastic systems.