  In this note, introducing notions of CH module, CH morphism and CH
connection, we define a meromorphic connection in the "$z$-direction" on
periodic cyclic homology of an $A_\infty$ category as a connection on
cohomology of a CH module. Moreover, we study and clarify compatibility of our
meromorphic connections under a CH module morphism preserving CH connections at
chain level. Our motivation comes from symplectic geometry. The formulation
given in this note designs to fit algebraic properties of open-closed maps in
symplectic geometry.
