Zobrazeno 1 - 10
of 40
pro vyhledávání: '"Anel, Mathieu"'
Autor:
Anel, Mathieu, Barton, Reid
We introduce homotopical variants of the axioms of countable and dependent choice for infinity-topoi and use them to give criteria for Postnikov completeness, revisiting a result of Mondal and Reinecke.
Comment: v2 improved somme lemmas, added s
Comment: v2 improved somme lemmas, added s
Externí odkaz:
http://arxiv.org/abs/2403.19772
Autor:
Anel, Mathieu, Weinberger, Jonathan
This is an expository note explaining how the geometric notions of local connectedness and properness are related to the $\Sigma$-type and $\Pi$-type constructors of dependent type theory.
Comment: Dedicated to Andr\'e Joyal to his 80th birthday
Comment: Dedicated to Andr\'e Joyal to his 80th birthday
Externí odkaz:
http://arxiv.org/abs/2402.00331
We define a commutative monoid structure on the poset of left-exact localizations of a higher topos, that we call the acyclic product. Our approach is anchored in a structural analogy between the poset of left-exact localizations of a topos and the p
Externí odkaz:
http://arxiv.org/abs/2308.15573
We revisit the work of To\"en--Vezzosi and Lurie on Grothendieck topologies, using the new tools of acyclic classes and congruences. We introduce a notion of extended Grothendieck topology on any $\infty$-topos, and prove that the poset of extended G
Externí odkaz:
http://arxiv.org/abs/2201.01236
Autor:
Anel, Mathieu
We show that the category of truncated spaces with finite homotopy invariants ($\pi$\=/finite spaces) has many of the features expected of an elementary \oo topos. It should be thought of as the natural higher analogue of the elementary 1-topos of fi
Externí odkaz:
http://arxiv.org/abs/2107.02082
Autor:
Anel, Mathieu, Calaque, Damien
Publikováno v:
Advances in Theoretical and Mathematical Physics, Volume 26 (2022), Number 6, Pages 1543-1583
We prove that the derived critical locus of a $G$-invariant function $S:X\to\mathbb{A}^1$ carries a shifted moment map, and that its derived symplectic reduction is the derived critical locus of the induced function $S_{red}:X/G\to\mathbb{A}^1$ on th
Externí odkaz:
http://arxiv.org/abs/2106.06625
Publikováno v:
In Journal of Pure and Applied Algebra March 2024 228(3)
Publikováno v:
Advances in Mathematics, Volume 400, 2022, 108268
We are developing tools for working with arbitrary left-exact localizations of $\infty$-topoi. We introduce a notion of higher sheaf with respect to an arbitrary set of maps $\Sigma$ in an $\infty$-topos $\mathscr{E}$. We show that the full subcatego
Externí odkaz:
http://arxiv.org/abs/2101.02791
We present a variant of the small object argument, inspired by Kelly, better suited to construct unique factorisation systems. Our main result is to compare it to the plus-construction involved in sheafification. We apply this to construct localizati
Externí odkaz:
http://arxiv.org/abs/2004.00731
Autor:
Anel, Mathieu, Lejay, Damien
We characterise the class of exponentiable $\infty$-toposes: $\mathcal X$ is exponentiable if and only if $\mathcal S\mathrm{h}(\mathcal X)$ is a continuous $\infty$-category. The heart of the proof is the description of the $\infty$-category of $\ma
Externí odkaz:
http://arxiv.org/abs/1802.10425