## New answers tagged monoidal-categories

2
votes

### Is the category of simplicial $R$-modules closed monoidal?

The category of simplicial $R$-modules is the category of $R$-modules in the closed symmetric monoidal category of simplicial sets. I wrote an answer last week with references explaining why such ...

1
vote

### Does the Gray tensor product exhibit Gray as a monoidal Gray-category?

If $V$ is a symmetric (or at least braided) monoidal closed category then there is a natural tensor product on the category of $V$-enriched categories. A $V$-enriched monoidal category is a (weak) ...

3
votes

Accepted

### One-object lax natural transformation

The two monoidal functors $F,G: M_{\mathcal K} \to M_{\mathcal L}$ select a way to make $M_{\mathcal L}$ into an $M_{\mathcal K}$-bimodule category. The data $(A_\alpha, \tilde{\alpha})$ is called a ...

3
votes

Accepted

### Dual objects in an abelian monoidal category

I get the sense that the OP is a relatively new user of MO and trying to learn about monoidal abelian categories. While the comment gives the core idea answering the OP's question, I wanted to point ...

4
votes

### Being (co)cartesian as a property (rather than structure) of a plain monoidal category

I don't have a counterexample to show that (3) is not superfluous, but I can provide some motivation for it. First, let us recall what is probably the most well known characterisation of cartesian ...

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