Sheaf of rings

A sheaf of rings assigns a ring $\mathcal{O}(U)$ to every open set, restriction homomorphisms to inclusions, and satisfies local identity and gluing. It supplies the local functions on a ringed space.

This is a ring-valued Sheaf (mathematics), with ring homomorphisms as restriction maps.

A sheaf of topological rings takes values in topological rings, with continuous restriction maps. For an open cover, the sheaf condition is an equalizer of the product of sections on the cover and the product on pairwise overlaps, in the category of topological rings. The structure sheaf of a formal scheme is an inverse limit of discrete structure sheaves with this topology.

// Target: algebra.bigb