• Corpus ID: 119329401

Regular and exact (virtual) double categories

@article{Schultz2015RegularAE,
  title={Regular and exact (virtual) double categories},
  author={Patrick Schultz},
  journal={arXiv: Category Theory},
  year={2015}
}
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… 
Algebraic Databases
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This work proposes an extension of the earlier set-valued functor model, making use of multi-sorted algebraic theories to incorporate concrete data in a principled way, and shows how all of the components of this model fit into a single double categorical structure called a proarrow equipment.
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References

SHOWING 1-8 OF 8 REFERENCES
Enriched categories as a free cocompletion
Basic category theory
Introduction 1. The language of categories 2. Limits 3. Adjoint functors 4. Generators and projectives 5. Categories of fractions 6. Flat functors and Cauchy completeness 7. Bicategories and
Framed bicategories and monoidal fibrations
In some bicategories, the 1-cells are `morphisms' between the 0-cells, such as functors between categories, but in others they are `objects' over the 0-cells, such as bimodules, spans, distributors,
Abstract pro arrows I
© Andrée C. Ehresmann et les auteurs, 1982, tous droits réservés. L’accès aux archives de la revue « Cahiers de topologie et géométrie différentielle catégoriques » implique l’accord avec les
A unified framework for generalized multicategories
Notions of generalized multicategory have been defined in numerous contexts throughout the literature, and include such diverse examples as symmetric multicategories, globular operads, Lawvere
Proarrows II
  • Cahiers de Topologie et Géométrie Différentielle Catégoriques
  • 1985
The formal theory of monads
  • Journal of pure and applied algebra
  • 1972