  We compare various different definitions of "the category of smooth objects".
The definitions compared are due to Chen, Fr\"olicher, Sikorski, Smith, and
Souriau. The method of comparison is to construct functors between the
categories that enable us to see how the categories relate to each other. This
produces a diagram of categories with the category of Fr\"olicher spaces
sitting at its centre. Our method of study involves finding a general context
into which these categories can be placed. This involves considering categories
wherein objects are considered in relation to a certain collection of standard
test objects. This therefore applies beyond the question of categories of
smooth spaces.
