Two proofs of the exponentiability of perfect maps are presented and compared to two other recent approaches. One of the proofs is an elementaryapproach including a direct construction of the exponentials. The other, implicit in the literature, uses internal locales in the topos of set-valued sheaves on a topological space.
Theory and Applications of Categories, Vol. 10, 2002, No. 5, pp 127-133 http://www.tac.mta.ca/tac/volumes/10/5/10-05.dvi http://www.tac.mta.ca/tac/volumes/10/5/10-05.ps http://www.tac.mta.ca/tac/volumes/10/5/10-05.pdf ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/5/10-05.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/10/5/10-05.psTAC Home