Homotopy excision theorem

In algebraic topology, the homotopy excision theorem offers a substitute for the absence of excision in homotopy theory. More precisely, let ${\displaystyle (X;A,B)}$ be an excisive triad with ${\displaystyle C=A\cap B}$ nonempty, and suppose the pair ${\displaystyle (A,C)}$ is (${\displaystyle m-1}$)-connected, ${\displaystyle m\geq 2}$, and the pair ${\displaystyle (B,C)}$ is (${\displaystyle n-1}$)-connected, ${\displaystyle n\geq 1}$. Then the map induced by the inclusion ${\displaystyle i:(A,C)\to (X,B)}$

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