Abstracts.2019.Kan

Kan extensions: the big picture of limits and colimits

by Joel Sjögren

Abstract

We will review by simple examples the notions of (co)limit, and explore how limits may organize into a Kan extension. Two faces of a dynamic intuition for functions (and functors) are described and employed: those of "growth" of a set (or category) and "forgetting", with composition corresponding to growth or forgetting in several steps. Of course an idea of growth would always be useful for understanding extension. Functoriality then allows us to analyze more complicated examples. The method is actually analogous to Gaussian elimination.

References

1. David Spivak. 2010. "Functorial data migration."
2. Marie La Palme Reyes, Gonzalo E. Reyes and Houman Zolfaghari. 2004. "Generic figures and their glueings."
3. Fosco Loregian. 2015. "Coend calculus."