2010/04/08 by Elemér E Rosinger, Elemer E Rosinger, Rosinger, Elemer E
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #General Mathematics (math.GM) #Homotopy and Cohomology in Algebraic Topology #Logic, programming, and type systems #math.GM
paper · pdf · doi:10.48550/arxiv.1004.1270
openalex publication_date 2010/04/08 · arxiv created 2010/04/09 · arxiv updated 2010/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
What makes sets, or more precisely, the category \bf Set important in Mathematics are the well known \it two specific ways in which arbitrary mappings f : X \longrightarrow Y between any two sets X, Y can \it fail to be bijections. Namely, they can fail to be injective, and/or to be surjective. As for bijective mappings they are rather trivial, since with some relabeling of their domains or ranges, they simply become permutations, or even identity mappings. To the above, one may add the \it third property of sets, namely that, between any two nonvoid sets there exist mappings. These three properties turn out to be at the root of much of the interest which the category \bf Set has in Mathematics. Specifically, these properties create a certain \it dynamics, or for that matter, lack of it, on the level of the category \bf Set and of some of its subcategories.