in a category is called quadrable , if there exists a cone
Let denote the span diagram category, that is, the category with three objects and two non-identity morphisms and .
Let be any category and let denote the diagonal into the functor category sending an object , where is the constant functor sending all objects and all morphisms of to and respectively.
For let denote the unique functor from the terminal category such that the unique object of maps to .
We say that a cospan in a category , that is, an object of the functor category is quadrable if there exists a cone for , that is, an object in the comma category .
Dually, we say that a span in a category , that is, an object of the functor category is coquadrable if there exists a cocone for , that is, an object in the comma category .
We say that a category is quadrable (resp. coquadrable) if all cospans (resp. spans) in are quadrable (resp. coquadrable).
Note on terminology
The term quadrable is supposed to be a translation of the French carrable , whose use is more wide-spread. It appears for instance in