Cartesian Double Categories and Profunctors
In this talk we will revisit the work that I did for my doctorate thesis "Cartesian Double Categories with an Emphasis on Characterizing Spans". We will see a comparison of the definition of Cartesian Double Categories given in the thesis with the definition of Cartesian Bicategories given by Carboni, Kelly, Walters, and Wood in 2008. We will specifically talk about Cartesian Double Categories that are also fibrant, and how we can use them to characterize Span-like double categories. Lastly, we will see how the Double Category of Profunctors was proven to be Cartesian and we will talk about the advantages of seeing profunctors as arrows of a double category in comparison to a bicategory.