论文标题
Eilenberg-Moore类别与PBW型定理之间的辅助
Adjunctions between Eilenberg-Moore categories and a PBW-type theorem
论文作者
论文摘要
最近，Dotsenko和Tamaroff表明，当$ \ Mathscr c $ $ t \ longrightArrow s $ monads $ \ mathscr c $的形态满足PBW-Property时，仅当它使$ s $将$ s $ s纳入免费的$ t $ -module。我们认为类别$ \ mathscr c $，$ \ mathscr d $，$ \ mathscr c $上的$ \ mathscr d $和$ \ mathscr d $上的$ \ mathscr c $上的$ \ s $ s $ sonad $ s $。我们表明，形态主义$ ϕ：（\ mathscr c，s）\ longrightArrow（\ mathscr d，t）$相对于相邻的$ψ$，在$ s $ sugn $ s $ s aff y Maths $ t $ -modules a $ t $ scr c $ \ n时，它的行为表现良好。
Recently, Dotsenko and Tamaroff have shown that a morphism of $T\longrightarrow S$ of monads over a category $\mathscr C$ satisfies the PBW-property if and only if it makes $S$ into a free right $T$-module. We consider an adjunction $Ψ=(G,F)$ between categories $\mathscr C$, $\mathscr D$, a monad $S$ on $\mathscr C$ and a monad $T$ on $\mathscr D$. We show that a morphism $ϕ:(\mathscr C,S)\longrightarrow (\mathscr D,T)$ that is well behaved with respect to the adjunction $Ψ$ has a PBW-property if and only if it makes $S$ satisfy a certain freeness condition with respect to $T$-modules with values in $\mathscr C$.
