Concepts of Category Theory

Category theory can be viewed as a metalanguage, whose main utility is to create a common framework for seemingly diverse notions. We have already used several of its concepts in disguise and will now proceed with the formal introduction. 

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Most concepts and constructions involving acyclic categories are introduced in analogy with those used in the context of posets. Often these translate into classical notions of category theory, while in some cases they 5deld notions that are not standard at all. 

We are aware that the categories of reception and diffusion have been criticized in recent years for their static conception of scientific theories, which are then transferred to passive recipients. Critics have proposed other terms, such as response or appropriation. " We allowed the individual authors to decide which term would be appropriate for their paper. 

Perhaps a well-motivated conception of the physical will proceed in terms of the laws and the categories associated with a few fundamental —for which read, general, and abstract theories in physics, especially quantum mechanics, relativity and their descendants. This seems fair, since presumably it is the explanatory performance of these great theories that underwrites the evidential standing of physicalism. This is indeed how physicalists have tended to identify the physical in a sense that allows it to contrast with the chemical, and be correspondingly informative (see for instance Quine 1981 Papineau 1990 Field 1992). 

Although we shall not deal with Hamilton-Jacobi theory here, the concept of a set of constants of the motion is vital to an understanding of the issue of intramolecular energy flow and statistical vs nonstatistical behavior. In essence, the number of global constants of the motion provides a method for grouping systems into general categories. 

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