Walking Wide Cospan

The I 𝐼 I -indexed walking wide cospan is a category whose objects are I ⊔ ⋆ I\sqcup\star , and whose non-identitty morphisms are of the form i → ⋆ → 𝑖 ⋆ i\to\star for i : I : 𝑖 𝐼 i:I .

Graphically, this category looks like

∙∙{\bullet}∙∙{\bullet}⋯⋯{\cdots}∙∙{\bullet}∙∙{\bullet}∙∙{\bullet}

A diagram over this category is a Wide Cospan.