A left bilinear morphism of pointed sets from $\webleft (X\times Y,\webleft (x_{0},y_{0}\webright )\webright )$ to $\webleft (Z,z_{0}\webright )$ is a map of sets
\[ f \colon X\times Y \to Z \]
satisfying the following condition:1,2
- Left Unital Bilinearity. The diagram
commutes, i.e. for each $y\in Y$, we have
\[ f\webleft (x_{0},y\webright ) = z_{0}. \]
1Slogan: The map $f$ is left bilinear if it preserves basepoints in its first argument.
2Succinctly, $f$ is bilinear if we have
\[ f\webleft (x_{0},y\webright ) = z_{0} \]
for each $y\in Y$.
