Tagged Questions

10
votes
12answers
746 views

Homological Algebra for Commutative Monoids?

Homological algebra for abelian groups is a standard tool in many fields of mathematics. How much carries over to the setting of commutative monoids (with unit)? It seems like ther …
0
votes
4answers
185 views

Splitting lemma under assumption of the axiom of choice

The splitting lemma says: Given a short exact sequence with maps $q$ and $r$: $0 \rightarrow A \overset{q}{\rightarrow} B \overset{r}{\rightarrow} C \rightarrow 0$ th …
6
votes
1answer
184 views

An “existence contra partition of unity” statement for integer matrices?

While reading a blog post on partitions of unity at the Secret Blogging Seminar the following question came into my mind. Let $n$ be a positive integer and let $B_1$ and $B_2$ be …