9 papers
Prime-Power Multiplicative Modular Monoid Morphisms
Joseph Atalaye, Liam Baker, Sophie Marques
We undertake a systematic study of multiplicative monoid morphisms between prime-power modular monoids and , fo…
Direct-product rigidity and factor reconstruction for monoids with zero
Joseph Atalaye, Liam Baker, Sophie Marques
We study direct products of monoids with zero and give a criterion under which their factors can be recovered from the multiplicative structure alone. While classical decomposition…
Generalized action monads and descent
Elena Caviglia, Sophie Marques, Luca Mesiti
We develop a monadic approach to actions of internal categories. Given an internal category, we construct a monad on a slice whose algebras are the actions of that internal categor…
Automorphism groups of direct products of multiplicative monoids of certain rings
Joseph Atalaye, Liam Baker, Sophie Marques
In this paper, we establish a rigidity result for automorphisms of multiplicative direct products of -rings which are total ring of fraction that have pairwise distinct cardinal…
Comparing the face rings of a boolean complex and its barycentric subdivision
Ben Blum-Smith, Sophie Marques
We consider the relationship between the Stanley--Reisner ring (a.k.a. face ring) of a simplicial or boolean complex and that of its barycentric subdivision. These rings share…
A note on gluing: a pillar of algebraic geometry
Sophie Marques, Damas Mgani
This paper examines the concept of gluing, placing it within its most general categorical context and tracing its foundational role in the broader architecture of algebraic geometr…
A study of a recursive sequence of polynomials revealing weighted Catalan Numbers
Sophie Marques, Elizabeth Mrema
This paper examines the recursive sequence of polynomials , defined by and for . It describes the field-theoretic m…
On the automorphism group of the monoid of the integers modulo a prime power
Joseph Atalaye, Liam Baker, Sophie Marques
This paper determines the structure of the automorphism group of the unit group \((U_{p^e}, \cdot)\) and the monoid \((\mathbb{Z}/p^e \mathbb{Z}, \cdot)\). For \( e \geq 5 \), we e…
A Categorical Perspective on Gluing
Sophie Marques, Damas Mgani
This paper introduces the concept of gluing in a general category, enabling us to define categories that admit glued-up objects. To achieve this, we introduce the notion of a gluin…