2018/05/04 by Charles Walker, Walker, Charles
Mathematics · #18C15 #18D05 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1805.01703
openalex publication_date 2018/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is well known that to give an oplax functor of bicategories 1→\mathscrC is to give a comonad in \mathscrC. Here we generalize this fact, replacing the terminal bicategory by any bicategory \mathscrA for which the composition functor admits generic factorisations. We call bicategories with this property generic, and show that for generic bicategories \mathscrA one may express the data of an oplax functor \mathscrA→\mathscrC much like the data of a comonad; the main advantage of this description being that it does not directly involve composition in \mathscrA. We then go on to apply this result to some well known bicategories, such as cartesian monoidal categories (seen as one object bicategories), bicategories of spans, and bicategories of polynomials with cartesian 2-cells.