Posts tagged ‘extension’

Extensions and homological algebra

If you ever followed a course in algebra, you may have heard about extensions of “things”. Most “things” fit in what is called a category, that is, an abstract structure remembering how to compose morphisms between these “things”, and sometimes what is the sum of such “things”, the kernel of a morphism: we are interested in the structure of abelian category, which is the framework of vector spaces, modules over a ring, sheaves of modules… An extension of A by B is an exact sequence

0 \to B \to E \to A \to 0

where B is the kernel, and A is the quotient (cokernel). The group of extensions \mathrm{Ext}^1(A,B) is the set of isomorphism classes of such exact sequences. (more…)


10 January 2009 at 12:02 pm Leave a comment