Definition
Category of unital topological rings
Hausdorff unital topological rings and continuous unit-preserving ring maps.
The category of unital topological rings used here consists of unital associative rings equipped with a Hausdorff topology for which addition, additive inversion, and multiplication are continuous. Morphisms are continuous maps preserving addition, multiplication, and . Identity maps and compositions preserve all these requirements.
Convention and comparison
The catalogue key topological-rings always uses this unit-preserving convention. Adeles and completions carry their specified topologies; forgetting topology leads to unital rings.