Decompositions of homomorphisms
Does imply axiom of choice?
Dualities for Stone algebras, double Stone algebras, and relative Stone algebras
Duality for some free modes
The paper establishes a duality between a category of free subreducts of affine spaces and a corresponding category of generalized hypercubes with constants. This duality yields many others, in particular a duality between the category of (finitely generated) free barycentric algebras (simplices of real affine spaces) and a corresponding category of hypercubes with constants.