Clonoids of Boolean functions with a linear source clone and a semilattice or 0- or 1-separating target clone

Extending Sparks's theorem, we determine the cardinality of the lattice of (C₁,C₂)-clonoids of Boolean functions for certain pairs (C₁,C₂) of clones of Boolean functions. Namely, when C₁ is a subclone (a proper subclone, resp.) of the clone of all linear (affine) functions and C₂ is a subclone of the clone generated by a semilattice operation and constants (a subclone of the clone of all $0$- or $1$-separating functions, resp.), then the lattice of (C₁,C₂)-clonoids is uncountable. Combining this fact with several earlier results, we obtain a complete classification of the cardinalities of the lattices of (C₁,C₂)-clonoids for all pairs (C₁,C₂) of clones on \0,1\.