Geodesic
Categories with slicing
Theory and applications of categories, Tome 22 (2009), pp. 97-135.

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

Prior work towards the subject of higher-dimensional categories gives rise to several examples of a category over $Cat$ to which the slice-category construction can be lifted universally. The present paper starts by supplying this last clause with a precise meaning. It goes on to establish for any such category a certain embedding in a presheaf category, to describe the image, and hence to derive conditions collectively sufficient for that functor to be an equivalence. These conditions are met in the foremost of the examples: the category of dendrotopic sets.
Classification : 18D99
Keywords: slice categories, presheaf category, polytopic sets 
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     author = {Thorsten Palm},
     title = {Categories with slicing},
     journal = {Theory and applications of categories},
     pages = {97--135},
     publisher = {mathdoc},
     volume = {22},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2009_22_a4/}
}
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Thorsten Palm. Categories with slicing. Theory and applications of categories, Tome 22 (2009), pp. 97-135. http://geodesic.mathdoc.fr/item/TAC_2009_22_a4/