Homotopy of magmas

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:

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