Definition
Category of topological groups
Hausdorff topological groups and continuous group homomorphisms.
The category of topological groups used here has Hausdorff topological groups as objects and continuous group homomorphisms as morphisms. Group multiplication and inversion are continuous in each object. Identities and composition are those of continuous maps.
Convention and comparison
An abstract group homomorphism need not be continuous. For finite-dimensional Lie groups, the catalogue also records the more specific real or complex Lie-group category, whose regularity convention is stated separately.