Limit

A limit for a Diagram
is a Terminal object of the Cone if it exists.

Dually we have a Colimit.

Example

Let be a Diagram.
We have a functor sending to the constant Diagram
with vertices and edges .
A Cone over with apex is a Natural Transformation
In fact is another name for the Comma Category

So has limits for all diagrams of shape
if and only if

has a right Adjoint.