Braiding on the module category and triangular structures

Let $H$ be a Hopf algebra over a field $k$ and let $H\text{-Mod}$ denote the category of all left $H$-modules and all $H$-linear maps, with tensor action and associators as in The module category of a bialgebra and its tensor action and Bialgebra module tensor actions and their coherence. A braiding on this category is a family of $H$-linear isomorphisms $c_{V,W}:V\otimes W⟶W\otimes V$ for all left $H$-modules $V,W$, natural in both variables, for which the following equalities hold after inserting the canonical associators of the module category: $c_{U,V\otimes W}=({\mathrm{id}}_V\otimes c_{U,W})\circ (c_{U,V}\otimes {\mathrm{id}}_W),c_{U\otimes V,W}=(c_{U,W}\otimes {\mathrm{id}}_V)\circ ({\mathrm{id}}_U\otimes c_{V,W})\mathrm{.}$ A quasitriangular structure $R$ is triangular if $R_{21}R=1_H\otimes 1_H$. A braiding is symmetric if $c_{W,V}\circ c_{V,W}={\mathrm{id}}_{V\otimes W}$ for every $V,W$. No finite-dimensional restriction is imposed on $H$ or on the modules in $H\text{-Mod}$.

For $R={\sum }_i{a}_i\otimes b_i$, the candidate braiding associated with $R$ is $c_{V,W}(v\otimes w)={\sum }_i{b}_{i}w\otimes a_{i}v$. Its well-definedness, module-linearity, naturality, hexagons, and the converse reconstruction from regular modules are supplied by A quasitriangular structure gives and is recovered from a module braiding ↗.