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Let F be an endofunctor of a category C. We prove isomorphism theorems for F -coalgebras under condition that the underlying category C is exact; that is, regular with exact sequences. Also, F is not assumed to preserve pullbacks.

Let A be a unital strict Banach algebra, and let K+ be the one-point compactification of a discrete topological space K. Denote by Open image in new window the weak tensor product of the algebra A and C(K+), the algebra of continuous functions on K+. We prove that if K has sufficiently large cardinality (depending on A), then the strict global dimension Open image in new window is equal to Open image in new window .