We generalize the Van Kampen theorem for unions of non-connected spaces, due to R. Brown and A. R. Salleh, to the context where families of subspaces of the base space B are replaced with a `large' space E equipped with a locally sectionable continuous map p: E -> B.
Keywords: Van Kampen Theorem, fundamental groupoid, locally sectionable map
2020 MSC: 20L05, 55Q05, 55R99
Theory and Applications of Categories, Vol. 36, 2021, No. 2, pp 48-64.