  We define involution algebroids which generalise Lie algebroids to the
abstract setting of tangent categories. As a part of this generalisation the
Jacobi identity which appears in classical Lie theory is replaced by an
identity similar to the Yang-Baxter equation. Every classical Lie algebroid has
the structure of an involution algebroid and every involution algebroid in a
tangent category admits a Lie bracket on the sections of its underlying bundle.
As an illustrative application we take the first steps in developing the
homotopy theory of involution algebroids.
