This extra structure arises from a lax symmetric monoidal functor F#92;colon#92;mathbf#123;C#125;#92;to#92;mathbf#123;D#125;; we use this functor to "decorate" each cospan with apex N#92;in#92;mathbf#123;C#125; with an element of F(N).
Source: wiktionary