  We develop a general theory of (extended) inner autoequivalences of objects
of any 2-category, generalizing the theory of isotropy groups to the
2-categorical setting. We show how dense subcategories let one compute isotropy
in the presence of binary coproducts, unifying various known one-dimensional
results and providing tractable computational tools in the two-dimensional
setting. In particular, we show that the isotropy 2-group of a monoidal
category coincides with its Picard 2-group, i.e., the 2-group on its weakly
invertible objects.
