*net-cohomology of posets*, a cohomological approach initiated and developed by J.E. Roberts [@Rob1], (see also [@Rob2; @Rob3] and references therein). Such an approach makes clear that the spacetime information which is relevant for the analysis of the DHR-sectors is the topological and the causal structure of Minkowski space (the Poincaré symmetry enters the theory only in the definition of the vacuum representation). In particular, the essential point is how these two properties are encoded in the structure of the index ${\mathcal{K}}$ as a partially ordered set (*poset*) with respect to *inclusion* order relation $\subseteq$. Representations satisfying (\[Int:1\]) are, up to equivalence, in 1-1 correspondence with 1-cocycles $z$ of the poset ${\mathcal{K}}$ with values in the vacuum representation of the net ${\mathscr{A}}_{\mathcal{K}}: {\mathcal{O}}\rightarrow {\mathcal{A}}({\mathcal{O}})$. Here ${\mathcal{A}}({\mathcal{O}})$ is the von Neumann algebra obtained by taking the bicommutant $\pi_o(\mathcal{R}({\mathcal{O}}))''$ of $\pi_o(\mathcal{R}({\mathcal{O}}))$. These 1-cocycles, which are nothing but the charge transporters of DHR-analysis, define a tensor $\mathrm{C}^*-$category ${\mathcal{Z}^1_t({\mathscr{A}}_{\mathcal{K}})}$ with a permutation symmetry and conjugation.\
The first investigation of sectors of DHR-type in a globally hyperbolic spacetime ${\mathcal{M}}$ has been done in [@GLRV]. First, the authors consider the net of local observables $\mathscr{R}_{{\mathcal{K}_{\diamond}}}$ indexed by the set ${\mathcal{K}_{\diamond}}$ of regular diamonds of ${\mathcal{M}}$: a family 