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Results tagged with monoidal-categories
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user 27013
4
votes
Quotient-free monoidal categories
Here are some additional thoughts and examples.
1) The argument presented in the OP applies whenever one has a monoidal category $(\mathsf{C},\otimes,1)$ in which the unit object $1$ is a separator a …
- 6,406
8
votes
Are there noncartesian monoidal categories with $A \otimes B = A \times B$?
Note: As pointed out by
Peter LeFanu Lumsdaine in the comments, the example constructed in this answer does not work in its current form, since naturality of the associator fails. (This only affects t …
- 6,406
8
votes
The dual of a dual in a rigid tensor category
TL;DR: $X\cong (X^*)^*$ is not necessarily true, and this seems to be a folklore result, mentioned e.g. in these notes by Müger on p.9 (found by Eduardo Pareja Tobes). However, finding explicit exampl …
- 6,406
6
votes
Accepted
Cartesian monoidal star-autonomous categories
[I'm going to assume $S' \cong S$, which holds in every symmetric monoidal $*$-autonomous category. (See e.g. Lemma 5.6 of this paper.) This applies here since cartesianness implies symmetry. Part of …
- 6,406