A note on the categorical van Kampen Theorem

In this note we show that for the canonical map X 1 + X 2 → X , from the topological sum of two subspaces X 1 , X 2 of X into X, to be of effective descent it is sufficient to be hereditarily a quotient map. Further, making use of the Brown–Janelidze categorical van Kampen Theorem, this translates into a van Kampen-type result.