Title: More on the Categorical and Differential Algebra of Commutative Rigs
Abstract: In this talk we’ll continue our friendly introduction to the differential algebraic theory of commutative rings by moving towards answering the question: “In what sense are the Kahler differentials functorial in the first place?” We’ll start by introducing fibrations and their morphisms, move on to briefly discussing the Grothendieck Construction (which allows one to move between fibrations and pseudofunctors, depending on taste), and then explain the sense in which taking the module of relative Kahler differentials is functorial in CRig.
The scope and vibes of this talk are meant to be more relaxed and informal, so if you’ve never met rigs before and want to get to know how their differential algebra works this is a fantastic opportunity (which of course I’d say, for I am the speaker) to see. Alternatively, this makes precise many constructions involving Kahler differentials which are at best ad-hoc in traditional commutative ring theory.
