Double Orthogonal Factorization Systems

arXiv (Cornell University)

Abstract

We define strict and lax orthogonal factorization systems on double categories. These consist of an orthogonal factorization system on arrows and one on double cells that are compatible with each other. Our definitions are motivated by several explicit examples, including factorization systems on double categories of spans, relations and bimodules. We then prove monadicity results for orthogonal factorization systems on double categories in order to justify our definitions. For fibrant double categories we discuss the structure of the double orthogonal factorization systems that have a given orthogonal factorization system on the arrows in common. Finally, we study the interaction of orthogonal factorization systems on double categories with double fibrations.

Authors 7

1. C. B. Aberlé
2. Elena Caviglia
   Affiliation as printed

   National Institute for Theoretical and Computational Sciences , South Africa

3. Matthew Kukla

   George Washington University

   Affiliation as printed

   The George Washington University , District of Columbia , USA

4. Rubén Maldonado

   Universidad Nacional Autónoma de México

   Affiliation as printed

   Universidad Nacional Autónoma de México , México

5. Luca Mesiti

   Stellenbosch University

   Affiliation as printed

   Stellenbosch University , South Africa , South Africa

6. Dorette Pronk

   Dalhousie University

   Affiliation as printed

   Dalhousie University , Halifax , Canada

7. Tanjona Fiononana Ralaivaosaona Aachen Leiden Institute of Advanced Computer Science

   Leiden University

   Affiliation as printed

   Leiden Institute of Advanced Computer Science , Leiden University , The Netherlands