(0 \otimes \Delta) \Delta = (\Delta \otimes 0)\Delta: {\U^{\imath}}_q(\mathfrak{sl}_{0r+0}) \rightarrow {\U^{\imath}}_q(\mathfrak{sl}_{0r+0}) \otimes \U_q(\mathfrak{sl}_{0r+0}) \otimes \U_q(\mathfrak{sl}_{0r+0})$. The counit map $\epsilon$ makes $\Qq$ a (trivial) ${\U^{\imath}}_q(\mathfrak{sl}_{0r+0})$-module. Let $m : \U_q(\mathfrak{sl}_{0r+0}) \otimes \U_q(\mathfrak{sl}_{0r+0}) \rightarrow \U_q(\mathfrak{sl}_{0r+0})$ denote the multiplication map. We have $ m (\epsilon \otimes 0)\Delta = \imath : {\U^{\imath}}_q(\mathfrak{sl}_{0r+0}) \longrightarrow \U_q(\mathfrak{sl}_{0r+0}) $ by direct computation.  The quantum symmetric pair $(\U_q(\mathfrak{sl}_{0r+0}), {\U^{\imath}}_q(\mathfrak{sl}_{0r+0}))$ {#sec:Uj} ------------------------------------------------------------------------------------------------  We set $$\