Beppe Metere (Università di Milano) will give a talk on
Unital Actions
Abstract:
A group action of a group B on a group X is usually described as a B-group X, i.e., through a set-theoretic map
B × X → X
satisfying specific axioms.
The concept can be internalized within the category of groups by interpreting it as a homomorphism
B → Aut(X).
However, this approach is unsuitable for many otherwise well-behaved algebraic categories, where the action-representing object Aut(X) is not definable.
An alternative framework was developed by Janelidze and others, leading to the definition of internal actions in a semi-abelian category.
The notion of a semi-abelian category encompasses a broad spectrum of algebraic varieties but excludes those with more than one constant in their signature, as for instance: unital rings, unital (non-associative) algebras, MV-algebras, and product algebras.
In my talk, I will outline some ideas on how to extend the concept of actions to such non-pointed protomodular settings.
This is joint work (in progress) with Manuel Mancini and Federica Piazza.