2024/06/19 by Pieter Hofstra, Hofstra, Pieter, Martti Karvonen +1
Computer Science · #18A30 #18G45 #18N10 #Category Theory (math.CT) #Cellular Automata and Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2406.13647
openalex publication_date 2024/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Abstract inner automorphisms can be used to promote any category into a 2-category, and we study two-dimensional limits and colimits in the resulting 2-categories. Existing connected colimits and limits in the starting category become two-dimensional colimits and limits under fairly general conditions. Under the same conditions, colimits in the underlying category can be used to build many notable two-dimensional colimits such as coequifiers and coinserters. In contrast, disconnected colimits or genuinely 2-categorical limits such as inserters and equifiers and cotensors cannot exist unless no nontrivial abstract inner automorphisms exist and the resulting 2-category is locally discrete. We also study briefly when an ordinary functor can be extended to a 2-functor between the resulting 2-categories.