• Corpus ID: 115163041

Categories of categories

@article{Pisani2007CategoriesOC,
  title={Categories of categories},
  author={Claudio Pisani},
  journal={arXiv: Category Theory},
  year={2007}
}
  • C. Pisani
  • Published 6 September 2007
  • Philosophy
  • arXiv: Category Theory
A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of finality (in particular terminal objects), discreteness and components, representability, colimits and universal arrows, seem to be best expressed in this very general setting. Furthermore, at this level we are in fact doing not only (E,M)-category theory but, in… 
Balanced category theory
Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple

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