**Puzzle 101**

We have a collection of sets which, due to unique arrows among themselves, necessarily forms a preorder.

As the arrow between members of this 'subcategory' are unique they do not carry any additional information.

The 'subcategory' has afferent and efferent arrows to other members of **Set**.

It seems like there should be something interesting about those arrows.

Given that we are constrained to members of **Set** the only member of this 'subcategory' seems to only be \\(\emptyset\\). The only inbound arrow being from itself, its identity arrow. It has a single morphism to every member of **Set**.

Are these properties of \\(\emptyset\\) only true for the category **Set**?

We have a collection of sets which, due to unique arrows among themselves, necessarily forms a preorder.

As the arrow between members of this 'subcategory' are unique they do not carry any additional information.

The 'subcategory' has afferent and efferent arrows to other members of **Set**.

It seems like there should be something interesting about those arrows.

Given that we are constrained to members of **Set** the only member of this 'subcategory' seems to only be \\(\emptyset\\). The only inbound arrow being from itself, its identity arrow. It has a single morphism to every member of **Set**.

Are these properties of \\(\emptyset\\) only true for the category **Set**?