...

ON EXTENSIONS AND COHOMOLOGY

by user

on
Category:

mathematics

12

views

Report

Comments

Transcript

ON EXTENSIONS AND COHOMOLOGY
ON EXTENSIONS AND COHOMOLOGY:
BAER SUMS AND SCHREIER-MAC LANE THEOREM
ANDREA MONTOLI
The first part of the talk will be focused on the Schreier-Mac Lane theorem in semi-abelian
action accessible categories [2, 3]: this theorem allows a description of the extensions with nonnecessarily abelian kernel in terms of cohomology. Then we will consider the non-semi-abelian
contexts of monoids and semirings: by results in [1], we will show that in these contexts it is
still possible to have Baer sums of “good” extensions with abelian kernel, namely of special
Schreier extensions.
References
[1] D. Bourn, N. Martins-Ferreira, A. Montoli, M. Sobral, Schreier split epimorphisms in monoids and in
semirings, Textos de Matemática (Série B), Departamento de Matemática da Universidade de Coimbra,
vol. 45 (2013).
[2] D. Bourn, A. Montoli, Intrinsic Schreier-Mac Lane extension theorem II: The case of action accessible
categories, J. Pure Appl. Algebra 216 (2012), 1757-1767.
[3] A.S. Cigoli, G. Metere, A. Montoli, Obstruction theory in action accessible categories, J. Algebra 385
(2013), 27-46.
Center for Mathematics of the University of Coimbra, FCT Project PTDC/MAT/120222/2010
1
Fly UP