• Corpus ID: 119329401

Regular and exact (virtual) double categories

  title={Regular and exact (virtual) double categories},
  author={Patrick Schultz},
  journal={arXiv: Category Theory},
We propose definitions of regular and exact (virtual) double categories, proving a number of results which parallel many basic results in the theory of regular and exact categories. We show that any regular virtual double category admits a factorization system which generalizes the factorization of a functor between categories into a bijective-on-objects functor followed by a fully-faithful functor. Finally, we show that our definition of exact double category is equivalent to an axiom proposed… 
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