We prove that the monoidal 2-category of cospans of ordinals and surjections is the universal monoidal category with an object X with a semigroup and a cosemigroup structures, where the two structures satisfy a certain 2-dimensional separable algebra condition.
Keywords: 2-categories, monoidal categories, structured objects
2000 MSC: 18D5, 18D10, 18D35
Theory and Applications of Categories,
Vol. 18, 2007,
No. 20, pp 631-653.
http://www.tac.mta.ca/tac/volumes/18/20/18-20.dvi
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http://www.tac.mta.ca/tac/volumes/18/20/18-20.pdf
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