Matt Kukla's personal webpage https://mkukla.net 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. https://mkukla.net/papers/dofs.pdf Added slides from ACT2024 talk at Oxford. https://mkukla.net/talks/act2024.pdf Added EPA 608 Universal certification to CV. https://mkukla.net/misc/cv_mkukla.pdf Update limit law slides to include recent talk at GW. https://mkukla.net/talks/limlaw-gw.pdf The positioning macros in MKPOV have been changed. https://mkukla.net/doc/mkpov/positioning.html My PGP key has been updated. https://mkukla.net/key_mkukla.txt UMD hosting deactivated following graduation. https://mkukla.net Added MAZE-1.PNG, MAZE-2.PNG https://mkukla.net/3d/7.html Updated CV to include BlueHalo position. Documentation pages for tofn at latest version. https://mkukla.net Additional documentation added to MVL pages. https://mkukla.net/doc/mvl See paper. https://mkukla.net/papers/cclo.pdf AirspyHF+ page updated. https://mkukla.net/K3JMK/airspyhf-linux.html RSS feed added to site. https://mkukla.net/rss.xml