2021/04/13 by Alan S. Cigoli, Cigoli, Alan S., Sandra Mantovani +5
Mathematics · #16B50 #16E40 #18D30 #18E13 #18E35 #18G45 #18G50 #20J06 #Abelian group #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Associative property #Categorical variable #Category Theory (math.CT) #Cohomology #Enriched category #FOS: Mathematics #Fibered knot #Functor #Group (periodic table) #Homotopy and Cohomology in Algebraic Topology #Kernel (algebra) #Mathematics #Morphism #Pure mathematics #Statistics #math.CT #msc:16B50 #msc:16E40 #msc:18D30 #msc:18E13 #msc:18E35 #msc:18G45 #msc:18G50 #msc:20J06
paper · pdf · doi:10.48550/arxiv.2104.06362
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/04/13 · arxiv updated 2021/04/14
We set up a fibred categorical theory of obstruction and classification of morphisms that specializes to the one of monoidal functors between categorical groups and also to the Schreier-Mac Lane theory of group extensions. Further applications are provided, as for example a classification of unital associative algebra extensions with non-abelian kernel in terms of Hochschild cohomology.