This abstract delivers a remark related to Topos Duality. We base ourselves on Alexander Grothendieck’s handwritten manuscript [from 1982] 103 Functorial "correspondences". Duality of topos: handwritten notes (nd). Rating No. 115 (14 p.), preserved at the Université de Montpellier archives (see https://grothendieck.umontpellier.fr/archives-grothendieck/#). We create our case directly from these 14 page scans, included in this abstract; we will use arrows, 2-cells and triangles that are present in the handwriting and we will transcribe them into bicategorical diagrams and formalize them in the ∞-categorical language accepted today. Bridging logics and geometry we believe our abstract can help advance Topos theory, through a deeper understanding of modern categorical logic, we regard a topos as the semantics of the theory. Duality then trades geometric morphisms for theory morphisms. In practice this informs howweinternalize our construct (e.g. synthetic algebraic geometry, cohesive/synthetic homotopy theory). Please note, Grothendieck through his notes, seems to sketch the clear functoriality required for such a bridge. Topos-theoretic Galois theory. Dualities between atomic/Boolean topoi and profinite group actions inspire contemporary refinements: étale homotopy types, profinite or condensed avatars, and generalized Galois categories. The handwritten notes do indicate when a topos is governed by a “Galois object,” which we reinterpret to study fundamental groupoids in ∞-topoi and stratified settings. His notes also appear to cover Morita equivalence for theories.( Two sites can present the same topos; two theories can be Morita-equivalent.) Grothendieck his notes emphasize the principle that equivalence of topoi, not presentation, is the relevant invariant for structural claims. We build further upon said angle, and provide new structural claims.