On the fibre product of incidence structures (Q1904256)

Consider the category \(\mathcal I\) of linear incidence structures given by a flag set \(F \subset P \times {\mathcal B}\), where \(P\) is the set of points and \(\mathcal B\) is the set of blocks. The author observes that \(F_1 \times F_2\) defines a fibre product (= pull back) in \(\mathcal I\). The fibre product of two Klingenberg structures with isomorphic quotients is again a Klingenberg structure of the same type (projective Klingenberg plane, circle plane with neighbourhood relation etc.). The construction of a fibre product is also applied to divisible designs.