Geodesic
Exponentiability in lax slices of Top
Theory and applications of categories, Tome 16 (2006), pp. 218-235.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We consider exponentiable objects in lax slices of Top with respect to the specialization order (and its opposite) on a base space B. We begin by showing that the lax slice over B has binary products which are preserved by the forgetful functor to Top if and only if B is a meet (respective, join) semilattice in Top, and go on to characterize exponentiability over a complete Alexandrov space B.
Classification : 18B30, 18A40, 18A25, 54C35, 54F05, 06F30
Keywords: exponentiable space, function space, lax slice, specialization order 
@article{TAC_2006_16_a10,
     author = {Susan Niefield},
     title = {Exponentiability in lax slices of {Top}},
     journal = {Theory and applications of categories},
     pages = {218--235},
     publisher = {mathdoc},
     volume = {16},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2006_16_a10/}
}
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Susan Niefield. Exponentiability in lax slices of Top. Theory and applications of categories, Tome 16 (2006), pp. 218-235. http://geodesic.mathdoc.fr/item/TAC_2006_16_a10/