2023/11/05 by Zurab Janelidze, Janelidze, Zurab
Mathematics · #18E40 #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2311.02666
openalex publication_date 2023/11/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we construct a wide class of examples of pretorsion theories in the sense of A. Facchini, C. Finocchiaro, and M. Gran. Given a category ℂ with a terminal object 1 and a category \mathbbD with an initial object 0, we show that (ℂ× 0,1×\mathbbD) is a pretorsion theory in ℂ×\mathbbD if and only if each morphism 0→ C in ℂ is a monomorphism, and each morphism D→ 1 in \mathbbD is an epimorphism. Here 0 denotes the set of initial objects in \mathbbD and 1 denotes the set of terminal objects in ℂ. We then remark that the result generalised to products of arbitrary pretorsion theories.