We give two related universal properties of the span construction. The first involves sinister morphisms out of the base category and sinister transformations. The second involves oplax morphisms out of the bicategory of spans having an extra property; we call these `jointed' oplax morphisms.
Keywords: Span, $\Pi_2$, Beck condition, adjoints, universal property, localizations, sinister morphisms, jointed oplax morphisms
2000 MSC: 18A40, 18D05
Theory and Applications of Categories,
Vol. 13, 2004,
No. 4, pp 61-85.
http://www.tac.mta.ca/tac/volumes/13/4/13-04.dvi
http://www.tac.mta.ca/tac/volumes/13/4/13-04.ps
http://www.tac.mta.ca/tac/volumes/13/4/13-04.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/13/4/13-04.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/13/4/13-04.ps