} \, , \quad \quad
\left\{ Q_{\alpha }, Q_{\beta }\right\} = \left( \Gamma ^{0}C\right) _{\alpha \beta }H \,  .
\end{split}$$ These are the (anti)commutation relations of the $\mathcal{N}=1$, $D=3$ super-Carroll algebra, which can also be obtained as a contraction of the $D=3$ super-Poincaré algebra (see [@Bergshoeff:2015wma] and references therein).

As $\ell \rightarrow \infty$, the $2$-form curvatures and the corresponding Bianchi identities become $$\label{curvadscarrollsuperF}
\begin{aligned}[c]
& \mathcal{R}^{ab} = d \omega^{ab} \, , \\
& \mathcal{K}^a = d k^a + \omega^a_{\phantom{a} b} k^b \, , \\
& R^a = d V^a + \omega^a_{\phantom{a}b} V^b \, , \\
& \mathcal{H} = d h + V^a k_a - \tfrac{1}{2} \bar{\psi} \Gamma^0 \psi   = \mathfrak{H} - \tfrac{1}{2} \bar{\psi} \Gamma^0 \psi  \,  , \\
& \Psi = d \psi + \tfrac{1}{4} \omega^{ab} \Gamma_{ab} \psi \, ,
\end{aligned}
\quad \quad
\begin{aligned}[c]
& d \mathcal{R}^{ab} = 0 \,  , \\
& D \mathcal{K}^a = \mathcal{R}^a_{\phantom{a} b} k^b \,   , \\
& D R^a = \mathcal{R}^a_{\phantom{a} b} V^b \,  , \\
& d \mathcal{H} = R^a k_a - V^a \mathcal{K}_a + \bar{\psi} \Gamma^0 \Psi \, , \\
& D \Psi = \tfrac{1}{4} \mathcal{R}^{ab} \Gamma_{ab} \psi \,  .
\end{aligned}$$ We can also take the $\ell \rightarrow \infty$ limit of the 