We introduce a class of toposes called" absolutely locally compact" toposes and of"
admissible" sheaf of rings over such toposes. To any such ringed topos $(\mathcal {T}, A) …

We study the topological full group of ample groupoids over locally compact spaces. We
extend Matui's definition of the topological full group from the compact to the locally compact …

In this thesis, we undertake the study of some classical set-based algebraic concepts in a
topos-theoretic setting. Actually, the topoi we are particularly interested in are the …

Let GG be a locally compact, Hausdorff, étale groupoid whose unit space is totally
disconnected. We show that the collection A (G) A (G) of locally-constant, compactly …

For every nuclear $\mathbb Z_\ell $-algebra $\Lambda $ and every small v-stack $ X $ we
construct an $\infty $-category $\mathcal D_ {\mathrm {nuc}}(X,\Lambda) $ of nuclear …

We define and study the cohomology theories associated to A_ ∞-algebras and cyclic A_ ∞-
algebras equipped with an involution, generalising dihedral cohomology to the A_ ∞ …

We study the groupoid C*-algebras associated to the equivalence relation induced by a
quotient map on a locally compact Hausdorff space. This C*-algebra is always a Fell …

Let $\mathcal {G} $ be a locally compact, non-compact group (we make the non-
compactness assumption, for the most part, simply to avoid trivialities). We show that under a …

As pointed out by I. Moerdijk and G. Reyes in [63], C∞-rings have been studied specially for
their use in Singularity Theory and in order to construct topos models for Synthetic …

Let $(\mathcal C,\otimes, 1) $ be an abelian symmetric monoidal category satisfying certain
conditions and let $ X $ be a scheme over $(\mathcal C,\otimes, 1) $ in the sense of To\" en …