Geodesic
Components, complements and the reflection formula
Theory and applications of categories, CT2006, Tome 19 (2007), pp. 19-40

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

We illustrate the formula $ (\downarrow p)x = \Gamma_!(x/p) $, which gives the reflection $\downarrow p$ of a category $p : P \to X$ over $X$ in discrete fibrations. One of its proofs is based on a ``complement operator" which takes a discrete fibration $A$ to the functor $\neg A$, right adjoint to $\Gamma_!(A\times-):Cat/X \to Set$ and valued in discrete opfibrations.Some consequences and applications are presented.

Classification : 18A99
Keywords: categories over a base, discrete fibrations, reflection, components, tensor, complement, strong dinaturality, limits and colimits, atoms, idempotents, graphs and evolutive sets 
Claudio Pisani. Components, complements and the reflection formula. Theory and applications of categories, CT2006, Tome 19 (2007), pp. 19-40. http://geodesic.mathdoc.fr/item/TAC_2007_19_a1/
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2007_19_a1/}
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