A note on the categorical van Kampen theorem
Brown and Janelidze identified the key property for obtaining the classical van Kampen theorem as a result on descent theory. In this note the author shows that for the canonical map \(X_1+X_2 \rightarrow X\), 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. Making use of the Brown-Janelidze categorical van Kampen theorem, this leads to a van Kampen-type result.
scientific article; zbMATH DE number 5888196