A categorical approach to operator semigroups

On Trotter–Kato type inductive limits in the category of C0-semigroups

“…We saw in Section 1.2 that each operator semigroup yields a generator, see Definition 1.4. In [16] also another related category has been introduced, namely C 0 SGG. The objects are tuples (X, A) where X is a Banach space and A : D(A) → X is the generator of a C 0 -semigroup.…”

“…A morphism between two objects (X, A) and (Y, B) is a map U ∈ L (X, Y ) with the properties that U x ∈ D(B) and U Ax = BU x for each x ∈ D(A), cf. [16,Def. 6].…”

“…Recently, the theory of C 0 -semigroups firstly has been approached by A. Ng by means of category theory, cf. [16]. We want to jump on the bandwagon and continue the study of this approach.…”