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The axioms of category theory arise in many contexts

  • structures and maps between them

  • structures and interpretations between them

  • theories and interpretations between them

  • theories and proofs between them

  • states and processes between them

  • words (as input/output) and programs (automata, algorithms) "between" them

  • points in a geometric space and paths between them (→ Feynman's path integrals?)

  • structures representing other structures, i.e. with representations between them (representation not only in the representation theoretic sense, but in a more general one)

I am looking for more examples of this kind.

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closed as not a real question by Thomas, Hagen von Eitzen, Norbert, rschwieb, Arkamis Oct 22 '12 at 15:09

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.