A note on the categorical van Kampen Theorem

摘要

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.