This same construction may be carried out if the 's are sets,John Rhodes & Benjamin Steinberg. The q-theory of Finite Semigroups. p. 133. . semigroups, topological spaces, rings, modules (over a fixed ring), algebras (over a fixed ring), etc., and the homomorphisms are morphisms in the corresponding category. The inverse limit will also belong to that category.
This same construction may be carried out if the 's are sets,John Rhodes & Benjamin Steinberg. The q-theory of Finite Semigroups. p. 133. . semigroups, topological spaces, rings, modules (over a fixed ring), algebras (over a fixed ring), etc., and the homomorphisms are morphisms in the corresponding category. The inverse limit will also belong to that category.