They can be used as a foundation for higher category theory .
They have been studied in the context of category theory.
In fact, much of category theory was developed as a language to study these similarities.
Joyal showed that they are a good foundation for higher category theory.
This is a special case of the universal property for products in category theory.
Categorical products are a particular kind of limit in category theory.
The above construction can be described nicely using the language of category theory.
He began the formulation of category theory in the 1940's.
In fact, this idea can be made precise using category theory.
The style is very abstract and makes heavy use of category theory.