2021/05/25 by Mamta Balodi, Abhishek Banerjee, Balodi, Mamta +1
Mathematics · #18E05 #47A53 #53C99 #58B34 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2105.11736
openalex publication_date 2021/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We replace a ring with a small \mathbb C-linear category C, seen as a ring with several objects in the sense of Mitchell. We introduce Fredholm modules over this category and construct a Chern character taking values in the cyclic cohomology of \mathcal C. We show that this categorified Chern character is homotopy invariant and is well-behaved with respect to the periodicity operator in cyclic cohomology. For this, we also obtain a description of cocycles and coboundaries in the cyclic cohomology of \mathcal C (and more generally, in the Hopf-cyclic cohomology of a Hopf module category) by means of DG-semicategories equipped with a trace on endomorphism spaces.