Grothendieck topology

A Grothendieck topology $J$ on the trace category $T$ is a coverage that regulates which families of morphisms constitute admissible covers. It determines when local data on recognition fibers can be glued into global data — the sheaf condition.

Axiom A3 of the QCHTTopos specification defines the Grothendieck topology. The pair $(T,J)$ forms the trace site, the foundational geometric structure of the topos.

See also: Grothendieck topology in sheaf theory.