#
The theory of core algebras: its completeness

##
Peter Freyd

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.

http://www.tac.mta.ca/tac/volumes/18/11/18-11.dvi

http://www.tac.mta.ca/tac/volumes/18/11/18-11.ps

http://www.tac.mta.ca/tac/volumes/18/11/18-11.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/18/11/18-11.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/18/11/18-11.ps

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