%Please do not modify this part%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\documentclass[a4paper,10pt]{amsart}  

\textwidth16cm \textheight20.5cm \oddsidemargin-0.1cm
\evensidemargin-0.1cm

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsthm}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage[inline]{enumitem}
\usepackage[dvips]{graphicx}
\usepackage{color}
\usepackage{comment}
\usepackage{hyperref}
\usepackage{url}
\usepackage{stackrel}
\usepackage{mathrsfs}
\usepackage{stmaryrd}
\usepackage{hyperref}
\usepackage{fancyhdr}
\usepackage[english]{babel}

\usepackage{background} % Per la filigrana

% Configurazione filigrana
\backgroundsetup{
  scale=0.5,            % dimensione logo
  color=black,           % colore
  opacity=0.08,           % trasparenza (0=trasparente, 1=opaco)
  %contents={\includegraphics[width=\paperwidth,height=\paperheight,keepaspectratio]{logo.png}},
  position={current page.center} % posizione centrata
}

\definecolor{blue-url}{RGB}{0,0,100}

\hypersetup{
	pdftitle={The Open Seminar},
	pdfmenubar=false,
	pdffitwindow=true,
	pdfstartview=FitH,
	colorlinks=true,
	linkcolor=blue-url,
	citecolor=blue-url,
	urlcolor=blue-url
}

\begin{document}                                
	
%The total length (including the references) should not exceed one page as pdf-file
		
\leftmargini16pt                                                           
\thispagestyle{empty}    
	
%1. Title of the talk inside \Large{} (mandatory)
	
\begin{center}
	\textbf{\Large{Category Theory meets Factorization Theory: the category \textsf{AtoMon}}}
\end{center}

%End of 1.

\vskip 0.2cm
	
% ---------------------
	
%2. Speaker's first name(s) and last name(s) inside \textsc{} (mandatory)

\begin{center}
	Salvatore~\textsc{Tringali} % example
\end{center}

\vskip 0.8cm
	
%End of 2
	
% ---------------------
	
%3. Abstract (mandatory)

\textit{Abstract.} %%%%% see the example below %%%%%

We introduce the category \textsf{AtoMon} of atomic monoids 
and atom-preserving homomorphisms as a non-full subcategory of the usual category 
of monoids and monoid homomorphisms. By computing all limits and colimits, we show 
that \textsf{AtoMon} is complete and cocomplete. We also explore arithmetic aspects 
of products and coproducts, deriving explicit formulas for key invariants related 
to factorization lengths. This work aims to build a bridge between category theory 
and factorization theory, offering a categorical framework for the study of atomic 
factorizations.

%End of 3.

% ---------------------

\vskip 0.5cm

%4. Academic bio (mandatory)

\textit{About the speaker.} %%%%% see the example below %%%%%

Salvatore ``Salvo'' Tringali is a full professor at the School of Mathematical 
Sciences of Hebei Normal University, where he has been since February 2019.

Before joining HebNU, he held research and teaching positions at the University 
of Graz (as a Lise Meitner fellow and lecturer), Nankai University (as a visiting 
professor), \'Ecole Polytechnique (as a postdoctoral researcher), Texas A\&M University 
at Qatar (as a research associate), and Sorbonne University (campus Pierre et Marie 
Curie, formerly Paris VI) as a Marie Curie fellow.

A recurring theme in his research is the interplay between arithmetic combinatorics 
and the structural properties of algebraic objects such as semigroups and rings. He 
has authored or coauthored about 40 papers, some of which have appeared in international 
journals such as Proceedings of the American Mathematical Society, Mathematical 
Proceedings of the Cambridge Philosophical Society, Pacific Journal of Mathematics, 
Journal of Algebra, and Israel Journal of Mathematics.

%End of 4

% ---------------------
	
%5. References (optional, but highly recommended)

\begin{thebibliography}{9}
\bibitem{Camp-Coss-Trin-2025} 
	F.\ Campanini, L.\ Cossu, and S.\ Tringali, 
	\textit{The category of atomic monoids}, 
	preprint (\url{https://arxiv.org/abs/2502.06610}).
\end{thebibliography}

%End of 5

\vskip 0.5cm                                                                                                                         	

% ---------------------

%6. Affiliation(s) & address(es) (including zip code, city & country) inside \textsc{} (mandatory)
	
{\footnotesize
\textsc{%
	School of Mathematical Sciences, Hebei Normal University | 050024 Shijiazhuang, China}%
}
	
%End of 6

% ---------------------
			
%7. Your email address (mandatory) and the url of your the webpage (optional), both inside \texttt{}
	
{\footnotesize%
	\textit{E-mail}: \texttt{salvo.tringali@gmail.com} 
	$\cdot$ 
	\textit{Web}: \url{https://salvo-tringali.github.io/home/}
}
	
%End of 7
\end{document}                                                                                                                       
