2020/09/14 by Yuki Goto, Goto, Yuki
Computer Science · #Advanced Algebra and Logic #FOS: Mathematics #Logic, programming, and type systems #Rings and Algebras (math.RA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2009.06741
openalex publication_date 2020/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we will explicitly construct cofree coalgebras, by first constructing cofree precoalgebras (namely those not necessarily coassociative or counital). Our approach does not impose any condition to the coefficient ring, which means, for example, it does not need to be a field. The main technique is to generate homomorphisms from certain type of infinite trees so that those constitute cofree precoalgebras.