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

Involution algebroids: a generalisation of Lie algebroids for tangent categories