On categories of merotopic, nearness, and lter algebras

We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of lter torsion free abelian groups is an epire ective subcategory of the category of lter abelian groups. The forgetful functor from the category of lter rings to lter monoids is essentially algebraic and the forgetful functor from the category of lter groups to the category of lters has a left adjoint.