On exponential objects among topological spaces and compactly generated topological spaces:
Susan Niefield, Cartesianness, PhD thesis, Rutgers 1978 (proquest:302920643)
Susan Niefield, Cartesianness: topological spaces, uniform spaces, and affine schemes., Journal of Pure and Applied Algebra, 23.2, 1982, pp. 147–167 (doi:10.1016/0022-4049(82)90004-4, pdf)
Susan Niefield, Cartesian inclusion: locales and toposes., Communications in Algebra 9:16 (1981) 1639–1671 (doi:10.1080/00927878108822672)
On exponential objects among internal groupoids in Top (topological groupoids):
Discrete Conduché functors are considered in
On quantales and quantic nuclei
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