Zhaohua Luo 4.3.
Extensive Topologies Suppose A is a coherent analytic category.
Any composite of locally direct mono is a locally direct mono. Since Y r is a direct factor of X and U r is a direct factor of Y r , U r is also a direct factor of X . This shows that any direct factor of Y is induced from a direct factor of X . Consequently any locally direct factor of Y is also a locally direct factor of X . X is called indirect if it does not factors through any proper direct mono.