We show that the category of \(C_1\) -cofinite modules for the universal \(N=1\) super Virasoro vertex operator superalgebra \(\mathcal {S}(c,0)\) at any central charge c is locally finite and admits the vertex algebraic braided tensor category structure of Huang–Lepowsky–Zhang. For central charges \(c^{\mathfrak {ns}}(t)=\frac{15}{2}-3(t+t^{-1})\) with \(t\notin \mathbb {Q}\) , we show that this tensor category is semisimple, rigid, and slightly degenerate, and we determine its fusion rules. For central charge \(c^{\mathfrak {ns}}(1)=\frac{3}{2}\) , we show that this tensor category is rigid and that its simple modules have the same fusion rules as \(\textrm{Rep}\,\mathfrak {osp}(1\vert 2)\) , in agreement with earlier fusion rule calculations of Milas. Finally, for the remaining central charges \(c^{\mathfrak {ns}}(t)\) with \(t\in \mathbb {Q}^\times \) , we show that the simple \(\mathcal {S}(c^{\mathfrak {ns}}(t),0)\) -module \(\mathcal {S}_{2,2}\) of lowest conformal weight \(h^{\mathfrak {ns}}_{2,2}(t)=\frac{3(t-1)^2}{8t}\) is rigid and self-dual, except possibly when \(t^{\pm 1}\) is a negative integer or when \(c^{\mathfrak {ns}}(t)\) is the central charge of a rational \(N=1\) superconformal minimal model. As \(\mathcal {S}_{2,2}\) is expected to generate the category of \(C_1\) -cofinite \(\mathcal {S}(c^{\mathfrak {ns}}(t),0)\) -modules under fusion, rigidity of \(\mathcal {S}_{2,2}\) is the first key step to proving rigidity of this category for general \(t\in \mathbb {Q}^\times \) .
