Clonoids of Boolean functions with essentially unary, linear, semilattice, or 0- or 1-separating source and target clones

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 essentially unary, linear, or 0- or 1-separating functions or semilattice operations. When such a (C₁,C₂)-clonoid lattice is uncountable, the proof is in most cases based on exhibiting a countably infinite family of functions with the property that distinct subsets thereof always generate distinct (C₁,C₂)-clonoids. In the cases when the lattice is finite, we enumerate the corresponding (C₁,C₂)-clonoids. We also provide a summary of the cardinalities of (C₁,C₂)-clonoid lattices of Boolean functions.