Theories of anything

Details Theories of anything Theories of anything

2012-02-03

arxiv.org/abs/1202.0684v2

Mathematics

Category Theory

Introduction added; many, though surely not all, howlers removed

Scientific paper

We suggest a generalization of \pi_0 for topological groupoids, which encodes incidence relations among the strata of the associated quotient object, and argue for its utility by example, starting from the orbit categories of the theory of compact Lie groups. One of the points of this note is that Thom's theory of structurally stable forms fits quite nicely with the categorical theory of databases developed recently by D. Spivak; the other is that the stratifications studied by Thom are closely related to the phase transitions studied in physics, and that the generalization of \pi_0 proposed here may be useful in their study: in particular, in organizing our understanding of the scaling laws which naturally accompany such phenomena, in the theory of condensed matter, biology, finance ...

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