Related papers: Finitely accessible arboreal adjunctions and Hinti…
We develop and investigate a general theory of representations of second-order functionals, based on a notion of a right comodule for a monad on the category of containers. We show how the notion of comodule representability naturally…
The Exponential Formula allows one to enumerate any class of combinatorial objects built by choosing a set of connected components and placing a structure on each connected component which depends only on its size. There are multiple…
Jones conjectures the arboreal representation of a degree two rational map will have finite index in the full automorphism group of a binary rooted tree except under certain conditions. We prove a version of Jones' Conjecture for quadratic…
A new construction to associate an internal category to an enriched one is presented. The key concept is that of extensive ambient category, and the construction follows the one that associates a category whose idempotents split to a given…
An extension $B\subset A$ of finite dimensional algebras is bounded if the $B$-$B$-bimodule $A/B$ is $B$-tensor nilpotent, its projective dimension is finite and $\mathrm{Tor}_i^B(A/B, (A/B)^{\otimes_B j})=0$ for all $i, j\geq 1$. We show…
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…
A-infinity algebras and categories are known to be the algebraic structures behind open string field theories. In this note we comment on the relevance of the homology construction of A-infinity categories to superpotentials.
A bi-Heyting algebra validates the G\"odel-Dummett axiom $(p\to q)\vee (q\to p)$ iff the poset of its prime filters is a disjoint union of co-trees (i.e., order duals of trees). Bi-Heyting algebras of this kind are called bi-G\"odel…
Building on work of Derksen-Fei and Plamondon, we formulate a conjectural correspondence between additive and monoidal categorifications of cluster algebras, which reveals a new connection between the additive reachability conjecture and…
We introduce a new notion of a relational word as a finite totally ordered set of positions endowed with three binary relations that describe which positions are labeled by equal data, by unequal data and those having an undefined relation…
We investigate the problem of type isomorphisms in a programming language with higher-order references. We first recall the game-theoretic model of higher-order references by Abramsky, Honda and McCusker. Solving an open problem by Laurent,…
A locally coherent exact category is a finitely accessible additive category endowed with an exact structure in which the admissible short exact sequences are the directed colimits of admissible short exact sequences of finitely presentable…
We introduce the notions of definable amenability and extreme definable amenability for groups in continuous structures and conduct an extensive analysis of them, drawing parallels with the classical first-order case. We characterize both…
We employ the theory of canonical extensions to study residuation algebras whose associated relational structures are functional, i.e., for which the ternary relations associated to the expanded operations admit an interpretation as…
Quasi-trees generalize trees in that the unique "path" between two nodes may be infinite and have any countable order type. They are used to define the rank-width of a countable graph in such a way that it is equal to the least upper-bound…
Linear categories naturally have several identification relations : isomorphisms, categorical equivalences and Morita equivalences. In this thesis, we construct the classifying stacks for these three relations ($\ukcatiso$, $\ukcateq$,…
We explore from an algebraic viewpoint the properties of the tree languages definable with a first-order formula involving the ancestor predicate, using the description of these languages as those recognized by iterated block products of…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
We prove a categorical duality between a class of abstract algebras of partial functions and a class of (small) topological categories. The algebras are the isomorphs of collections of partial functions closed under the operations of…
Extensions of Stone-type dualities have a long history in algebraic logic and have also been instrumental in proving results in algebraic language theory. We show how to extend abstract categorical dualities via monoidal adjunctions,…