Comultiplication

Definition
Suppose $$(X,x_0)$$ is a based topological space. A comultiplication on this space is a continuous based map:

$$(X,x_0) \to (X,x_0) \vee (X,x_0)$$

where $$\vee$$ denotes the defining ingredient::wedge sum of topological spaces ans continuous based map means continuous map that sends basepoint to basepoint.