Here's an idea. Let \(A_{x\in \mathbb R} \) a \(\mathbb R\)-graded monoid. \(d:A\to \mathbb R\) satisfies \(d(f\cdot g)=d(f)+d(g)\).
Let \(\mathbb T\) be circle group, whose elements are to be seen as complex numbers \(e^{i\theta}\). Assume \(\mathbb T\) can be represented in \(A_0\) then we are enriching the graded monoid \(A_x\) with an action \(\mathbb T \times A_x\to A_x\) for each \(x\in\mathbb R\).
I wonder if the condition \(\displaystyle g\cdot f= e^{ d(f)d(g) \pi i}\cdot f\cdot g \) can give us what we want...
Let \(\mathbb T\) be circle group, whose elements are to be seen as complex numbers \(e^{i\theta}\). Assume \(\mathbb T\) can be represented in \(A_0\) then we are enriching the graded monoid \(A_x\) with an action \(\mathbb T \times A_x\to A_x\) for each \(x\in\mathbb R\).
I wonder if the condition \(\displaystyle g\cdot f= e^{ d(f)d(g) \pi i}\cdot f\cdot g \) can give us what we want...
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)
