2022/07/27 by Gintaras Valiukevičius, Valiukevičius, Gintaras · 4 citations
Mathematics · #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2207.13379
openalex publication_date 2022/07/27 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28
We are checking the closed categories beginning with the category of sets and ending with the category of categories. The novelty is a generalizing the notion of adjoint functors to the joint pair of functors in the category of directed graphs. We have described for what condition we get a bijective name mapping for graphs transports. Graphs aren't instances of categories, however we believe that new notion of functors joint pair will become important also for the categorical studies. As an example of future applications we introduce the notion of relator to some tensor product.