All Questions

Let $A : = \mathbb{C}[x_1, \ldots, x_n],$ $A_q : =\mathbb{C}_q[x_1, \ldots, x_n] = \mathbb{C} \langle x_1, \ldots, x_n \rangle / (x_ix_j = q x_jx_i)$. By Koszul resolution I mean $$\ldots \to A \...

Let $R$ be any commutative ring, let $V^\bullet$ and $W^\bullet$ be (co)chain complexes of $R$-modules, indexed cohomologically. We can also assume that they have both cohomology in nonpositive ...

I'm fairly new to thinking about homological algebra and chain complexes in their own right, i.e outside of isolated examples such as for constructing simplicial homology, or for computing $Ext$ ...

Does it exist a different notion of Hermitian metric for complexes of vector bundles, besides the obvious data of a metric for each vector bundle? Same question for connections. In particular is there ...

Usually we define singular homology via the complex of singular chains: $$C_\ast(X)=\bigoplus_{n\geq 0}\mathbb Z\langle\sigma:\Delta^n\to X\rangle$$ where the right hand side denotes the free abelian ...

Just as the fact that a categorification of $\mathbb{N}$ is the category of finite dimensional vector spaces, a categorification of $\mathbb{Z}$ (in my mind) is the category of bounded cochain ...