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FORMAL THEORY OF MONADS, ADJUNCTIONS, ENTWINING STRUCTURES AND GALOIS THEORY
- Speaker(s)
- STEFAAN CAENEPEEL
- Affiliation
- Vrije Universiteit Brussel, Belgium
- Date
- Oct. 25, 2023, 5:15 p.m.
- Information about the event
- 405 IMPAN & ZOOM
- Seminar
- North Atlantic Noncommutative Geometry Seminar
Brzeziński (2002) introduced Galois theory for corings with a fixed grouplike element. El Kaoutit and Gómez-Torrecillas (2003) generalized this to so-called comatrix corings. This establishes a general framework for existing Galois theories: classical Galois theory, Hopf-Galois theory, Galois theory for partial actions, Hopf-Galois theory for weak Hopf algebras, etc. Since (co)rings are (co)monads in the bicategory of algebras, bimodules, and bimodule maps, the aforementioned general framework has a bicategorical flavour. The idea of this talk is to provide a new framework for Galois theory using 2-categories and bicategories. It is well known that algebraic and categorical notions, like (co)algebras, Frobenius algebras, entwining structures, adjunctions, can be introduced in 2-categories. For example, algebras in a 2-category are usually called monads, and can be organized into a new 2-category in two different ways (Street, 1971). We review this theory and provide several new 2-categorical applications. Under the assumption that certain (co)equalizers exist in the categories that build up the given 2-category, we generalize Galois theory for comatrix corings.
