Grothendieck groups of 2-rigs as lambda rings

Abstract: This talk will report on recent joint work with John Baez and Joe Moeller. We introduce a notion of 2-rig as a way of categorifying the usual notion of rig (ring without negatives); examples include categories of group representations, categories of vector bundles over spaces, categories of coherent sheaves over projective varieties, and many others. We describe Schur functors on general 2-rigs, and indicate how the free 2-rig on one generator encodes Schur functors on 2-rigs. Finally, we indicate how the Grothendieck group of a 2-rig yields a lambda ring, where the theory of lambda-rings is a “plethory” obtained by decategorifying a conceptually simple 2-plethory that is associated with the free 2-rig.

category theory

Audience: researchers in the topic

ItaCa Fest 2021

Series comments: ItaCa Fest is an online webinar aimed to gather the community of ItaCa.