Title

We give a general construction of realization
functors for t-structures on the base of a strong stable
derivator. In particular, given such a derivator **D**, a
t-structure **t**=(**D**≤0,**D**≥0) on
the triangulated category **D**(**1**), and letting **A**=**D**≤0∩**D**≥0 be
its heart, we construct a morphism of prederivators

real**t **: **Der****A **⟶**D**,

where