All Questions

Question (idea): Is there a notion of tensor product of chain complexes in a $\mathcal{V}$-enriched monoidal category $\mathcal{C}$, for $\mathcal{V}$ a linear symmetric monoidal category? Let me ...

As far as I understand, an arbitrary abelian category is not enriched over itself, for example, $\mathrm{ChainComplex}(\mathrm{Ab})$ is, right? On the other hand, the categories $\mathrm{Mod}(R)$ (in ...

Let $V$ be a graded vector space over $\mathbb{k}$ and $V[1]$ its odd degree shift. Given $k$, $l\in \mathbb{N}_0$, is there a natural way to define the following map, $$ \psi: \hom_{\mathbb{k}}(V^{\...

Recently, Jade Master asked whether the tensor product of chain complexes could be viewed as a special case of Day convolution. Noting that chain complexes may be viewed as $\mathsf{Ab}$-functors from ...

dg: is for differential graded Suppose that $F: C\rightarrow D$ is a dg-functor between small dg-categories such that: F: Objects of $C$ $\rightarrow$ Objects of $D$ is injective. $Hom_{C}(a,b)\...