gin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mclose">)</span></span></span></span>—the category of bimodules over the enveloping algebra—becomes lax duoidal.
Its bimonoids are known as (Takeuchi) bialgebroids over the base algebra <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><m