Geodesic
Internal Hom Functors for Polarities
Canadian mathematical bulletin, Tome 22 (1979) no. 2, pp. 187-202

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The notion of functionality for an internal horn functor H in a concrete category K was introduced in Banaschewski and Nelson [1], formalizing the condition that the structure on the H(A, B) is "pointwise" structure on sets of functions. 
Nelson, Evelyn. Internal Hom Functors for Polarities. Canadian mathematical bulletin, Tome 22 (1979) no. 2, pp. 187-202. doi: 10.4153/CMB-1979-026-7
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     author = {Nelson, Evelyn},
     title = {Internal {Hom} {Functors} for {Polarities}},
     journal = {Canadian mathematical bulletin},
     pages = {187--202},
     year = {1979},
     volume = {22},
     number = {2},
     doi = {10.4153/CMB-1979-026-7},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1979-026-7/}
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