Tootfinder

Finite coproducts, coregularity and coexactness for profinite interior algebras
Matteo De Berardinis
https://arxiv.org/abs/2509.13058 https://arxiv.org/pdf…

Finite coproducts, coregularity and coexactness for profinite interior algebras
In previous articles, we showed that the category of profinite $L$-algebras (where $L$ is a normal modal logic with the finite model property) is monadic over $\textbf{Set}$. Then, we developed sequent calculi for extensions of the language of $L$ with infinitary conjunctions and disjunctions, proving completeness with respect to profinite $L$-algebras and relating syntactic properties of the calculi with regularity/exactness properties of the category opposite to profinite $L$-algebras. In thi…

Massey products and unipotent extensions with restricted ramification
Oussama Hamza (HIT), Donghyeok Lim (FEMTO-ST, UMLP), Christian Maire (FEMTO-ST, UMLP)
https://arxiv.org/abs/2508.03233

Massey products and unipotent extensions with restricted ramification
We fix a prime p and construct new cases of pro-p extensions of number fields with restricted ramification and splitting, whose Galois groups decompose as coproducts of pro-p absolute Galois groups of local fields. As a consequence, these pro-p extensions satisfy the strong Massey vanishing property and thus admit large unipotent quotients.

The category of propositional deductive systems
Ciro Russo
https://arxiv.org/abs/2508.19426 https://arxiv.org/pdf/2508.19426…

The category of propositional deductive systems
We define the category $\mathcal{QM}$ of quantales and their modules and prove the existence of coproducts, and the one of pushout and amalgamated coproducts under certain conditions. Then we define the non-full subcategory $\mathcal{DS}_0$, of propositional deductive systems, show that it is equivalent to the one of ``real'' propositional logics whose morphisms are interpretations (modulo a language translation, when needed), and prove that the coproduct in $\mathcal{DS}_0$ is precisely the de…

Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach
Loic Foissy, Xiao-Song Peng, Yunzhou Xie, Yi Zhang
https://arxiv.org/abs/2508.18658 https://

Moerdijk Hopf algebras of decorated rooted forests: an operated algebra approach
In this paper, we first endow the space of decorated planar rooted forests with a coproduct that equips it with the structure of a bialgebra and further a Moerdijk Hopf algebra. We also present a combinatorial description of this coproduct, and further give an explicit formulation of its dual coproducts through the newly defined notion of forest-representable matrices. By viewing the Moerdijk Hopf algebra within the framework of operated algebras, we introduce the notion of a multiple cocycle H…