The core of a category (first defined in ``Core algebra revisited'' Theoretical Computer Science, Vol 375, Issues 1-3, pp 193-200) has the structure of an abstract core algebra (first defined in the same place). A question was left open: is there more structure yet to be defined? The answer is no: it is shown that any operation on an object arising from the fact that the object is the core of its category can be defined using only the constant and two binary operations that appear in the definition of abstract core algebra. In the process a number of facts about abstract core algebras must be developed.
Keywords: core, cored category, abstract core algebra, critical lemma, no-lost-variables, base cancellation
2000 MSC: 18A40
Theory and Applications of Categories,
Vol. 18, 2007,
No. 11, pp 303-320.