It relies on the universal properties of gas, a big advance from just a particular substance.

Put another way, is a logical conjunction of all universal properties that has.

There is no field satisfying a free universal property for a given set.

The direct limit can be defined in an arbitrary category by means of a universal property.

This has a universal property for morphisms from S to a group.

This is a special case of the universal property for products in category theory.

This article gives a general treatment of universal properties.

Thus, the task is to find universal properties that uniquely determine the objects of interest.

To be more explicit, the following universal property can be used.

Therefore by universal property of free product we will get a unique map and .