2023/09/20 by Mykola Khrypchenko, Khrypchenko, Mykola, Francisco Klock +1 · 1 citation
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.2309.11300
Let M be a monoid, \mathscrC a category with pullbacks and X an object of \mathscrC. We introduce the notion of a partial action α of M on X and study the globalization question for α. If α admits a reflection in the subcategory of global actions, then we reduce the problem to the verification that a certain diagram is a pullback in \mathscrC. We then give a construction of such a reflection in terms of a colimit of a certain functor with values in \mathscrC. We specify this construction to the case of categories admitting certain coproducts and coequalizers.