Homotopy of magmas

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Definition

Let (S,*) and (T,\cdot) be magmas (i.e., S and T are sets with binary operations * and \cdot). A homotopy of magmas from (S,*) to (T,\cdot) is a triple (\alpha,\beta,\gamma) of maps from S to T such that for all g,h \in S, we have:

\alpha(g) \cdot \beta(h) = \gamma(g * h)