  We develop a theory of gapped domain wall between topologically ordered
systems in two spatial dimensions. We find a new type of superselection sector
-- referred to as the parton sector -- that subdivides the known superselection
sectors localized on gapped domain walls. Moreover, we introduce and study the
properties of composite superselection sectors that are made out of the parton
sectors. We explain a systematic method to define these sectors, their fusion
spaces, and their fusion rules, by deriving nontrivial identities relating
their quantum dimensions and fusion multiplicities. We propose a set of axioms
regarding the ground state entanglement entropy of systems that can host gapped
domain walls, generalizing the bulk axioms proposed in [B. Shi, K. Kato, and I.
H. Kim, Ann. Phys. 418, 168164 (2020)]. Similar to our analysis in the bulk, we
derive our main results by examining the self-consistency relations of an
object called information convex set. As an application, we define an analog of
topological entanglement entropy for gapped domain walls and derive its exact
expression.
