  Forking is a central notion of model theory, generalizing linear independence
in vector spaces and algebraic independence in fields. We develop the theory of
forking in abstract, category-theoretic terms, for reasons both practical (we
require a characterization suitable for work in $\mu$-abstract elementary
classes, i.e. accessible categories with all morphisms monomorphisms) and
expository (we hope, with this account, to make forking accessible - and useful
- to a broader mathematical audience). In particular, we present an axiomatic
definition of what we call a stable independence notion on a category and show
that this is in fact a purely category-theoretic axiomatization of the
properties of model-theoretic forking in a stable first-order theory.
