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   {"id":"aristoteMulticategoricalFrameworkMinimization2024","abstract":"Joint work with Daniela Petrişan. This paper provides a unifying category-theoretic framework for minimization and learning algorithms for bottom-up tree automata with effects. Our aim is two-fold: encompass existing algorithms for various forms of tree automata – deterministic bottom-up tree automata, residual finite tree automata, tree automata weighted over a field – and instantiate the abstract framework in order to obtain new results – tree automata weighted over principal ideal domains (PIDs).","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteMulticategoricalFrameworkMinimization2024","container-title":"Tree Automata","event-place":"Bordeaux, France","event-title":"Highlights of Logic, Games and Automata (Highlights 2024)","genre":"conference","issued":{"date-parts":[["2024",9,18]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/1003/uploads/c415dcc8a1e22c5d91cb91cfd8d6d55f/minimal-tree-automata.pdf","title":"Multicategorical framework for minimization and learning of bottom-up tree automata with effects","type":"speech","URL":"https://highlights-conference.org/2024/"},
   {"id":"aristoteNumberRingsAre2025","abstract":"We study automata weighted over number rings, that is, rings of integers in an algebraic number field.\n\nWe show that number rings are what we call \"almost strong Fatou\": if an n-state automaton weighted in a number field recognizes an integer-valued series, then it admits an equivalent n+1-state automaton weighted in the corresponding ring of integers.\n\nWe give a polynomial time procedure for computing such an n+1-state integer-weighted automaton, and show that deciding whether this automaton is minimal among all equivalent integer-weighted automata is as hard as PIP, a problem for which the best known algorithm is in quantum polynomial time.\n\nThis procedure provides a reduction between learning problems for automata weighted in number rings and in fields, and we show that it is an instance of a more general, abstract reduction procedure between learning problems for automata valued in two categories related by well-behaved functors.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteNumberRingsAre2025","event-place":"Marseille, France","event-title":"Combinatorics, Automata and Number Theory 2025","genre":"conference","issued":{"date-parts":[["2025",9,29]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/73d3ba029f37d98b7090cce6fd81d8f1/number-rings-almost-strong-fatou.pdf\nposter: https://gitlab.math.univ-paris-diderot.fr/-/project/996/uploads/6c9a3e6d87931780518a540aabb432de/removing-fractions.pdf","title":"Number rings are almost strong Fatou","type":"speech","URL":"http://www.discmath.ulg.ac.be/CANT2025/"},
   {"id":"aristoteOpenPowerObjectsCategories2025","abstract":"https://conference.math.muni.cz/ct2025/data/uploads/abstracts/aristote.pdf","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteOpenPowerObjectsCategories2025","event-place":"Brno, Czech Republic","event-title":"International Category Theory Conference (CT 2025)","genre":"conference","issued":{"date-parts":[["2025",7,18]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/1062/uploads/620105dfc6c8ec7fef78737368585a25/open-powerobjects-algebras.pdf","title":"Open Power-Objects in Categories of Algebras","type":"speech","URL":"https://conference.math.muni.cz/ct2025/"},
+  {"id":"aristoteProfunctorialAlgebras2026a","abstract":"Joint work with Umberto Tarantino. We provide a bicategorical generalization of Barr's landmark 1970 paper, in which he describes how to extend Set-monads to relations and uses this to characterize topological spaces as the relational algebras of the ultrafilter monad. With two-sided discrete fibrations playing the role of relations in a bicategory, we first characterize, in terms of exact squares, when pseudomonads on a bicategory extend to its bicategory of two-sided discrete fibrations. As a wide class of examples, we show that every Set-monad induces a pseudomonad on the 2-category of categories satisfying our criterion and thus extending to profunctors. Among these, we then focus on the ultracompletion pseudomonad, whose pseudoalgebras are ultracategories: we characterize the normalized lax algebras of its profunctorial extension as ultraconvergence spaces, a recently-introduced categorification of topological spaces.","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteProfunctorialAlgebras2026a","event-place":"Gif-sur-Yvette, France","event-title":"LHC days","genre":"seminar","issued":{"date-parts":[["2026",6,17]]},"language":"en","note":"slides: https://smimram.gitlabpages.inria.fr/lhc/slides/2026/aristote.pdf","title":"Profunctorial algebras","type":"speech","URL":"https://smimram.gitlabpages.inria.fr/lhc/journees.html"},
   {"id":"aristoteWeakDistributiveLaws2024","abstract":"https://iiia.csic.es/tacl2024/abstracts/conference/contributed/TACL_2024_paper_118.pdf","author":[{"family":"Aristote","given":"Quentin"}],"citation-key":"aristoteWeakDistributiveLaws2024","event-place":"Barcelona, Spain","event-title":"Topology, Algebra, and Categories in Logic (TACL 2024)","genre":"conference","issued":{"date-parts":[["2024",7,4]]},"language":"en","note":"slides: https://gitlab.math.univ-paris-diderot.fr/-/project/1057/uploads/a2a13506a3034d6713fa0786adbc9ebf/wdl-powerspaces-scs.pdf","title":"Weak distributive laws between powerspaces over stably compact spaces","type":"speech","URL":"https://iiia.csic.es/tacl2024/"}
 ]