Definition of "cospan"

This extra structure arises from a lax symmetric monoidal functor F : C → D {\displaystyle F\colon \mathbf {C} \to \mathbf {D} } ; we use this functor to "decorate" each cospan with apex N ∈ C {\displaystyle N\in \mathbf {C} } with an element of F ( N ) {\displaystyle F(N)} .

2016, Kenny Courser, “A bicategory of decorated cospans”, in arXiv‎