We compare various different definitions of "the category of smooth objects". The definitions compared are due to Chen, Frolicher, 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. 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.
Keywords: generalised smooth spaces
2000 MSC: Primary: 58A40, Secondary: 18F15
Theory and Applications of Categories, Vol. 25, 2011, No. 4, pp 64-117.