Title: The Differential Algebra of Commutative Rigs: Derivations and Differentials
Abstract: In the last talk I gave on commutative rigs, we got to know a bit about how the categories of commutative rig algebras and their modules interact together. In this talk we’ll continue towards our ultimate goal of understanding the differential/algebraic geometry of rigs by getting to know how the theory of derivations and differentials interacts with rigs. I’ll start by recalling our main cast of characters, define what it means to be a derivation, define the rig module of Kahler differentials, and then start to show some of the properties these modules have. Depending on time we’ll discuss how to encode derivations as solutions to specific lifting problems and/or in what sense the Kahler differentials construction is functorial. This talk will be relatively gentle in delivery, so all are encouraged to come and see how cool rigs are!
