## Posts tagged ‘baer sum’

### 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…)