Geodesic
“Topologically Indexed Function Spaces and Adjoint Functors”
Canadian mathematical bulletin, Tome 25 (1982) no. 2, pp. 169-178

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Let Top denote the category of topological spaces and continuous maps. In this paper we discuss families of function spaces indexed by the elements of a topological space T, and their relationship to the characterization of right adjoints Top/S → Top/T, where S is also a topological space. After reducing the problem to the case where S is a one-point space, we describe a class of right adjoints Top → Top/T, and then show that every right adjoint Top → Top/T is isomorphic to one of this form. We conclude by giving necessary and sufficient conditions for a left adjoint Top/T → Top to be isomorphic to one of the form − XTY, where Y is a space over T, and xT denotes the fiber product with the product topology. 
Niefield, S. B. “Topologically Indexed Function Spaces and Adjoint Functors”. Canadian mathematical bulletin, Tome 25 (1982) no. 2, pp. 169-178. doi: 10.4153/CMB-1982-023-1
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     author = {Niefield, S. B.},
     title = {{\textquotedblleft}Topologically {Indexed} {Function} {Spaces} and {Adjoint} {Functors{\textquotedblright}}},
     journal = {Canadian mathematical bulletin},
     pages = {169--178},
     year = {1982},
     volume = {25},
     number = {2},
     doi = {10.4153/CMB-1982-023-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-023-1/}
}
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