Atomic finite-surjection site
= Atomic finite-surjection site
Use a small skeleton of nonempty finite sets and surjections, with every nonempty sieve covering. Fiber-product projections are surjections, so the atomic coverage exists. Surjections are effective quotients of their kernel pairs, making the site <subcanonical>. Its sheaves admit the <primitive decomposition of an atomic finite-surjection sheaf>.