Geodesic
Covariant presheaves and subalgebras
Theory and applications of categories, Tome 25 (2011), pp. 342-367.

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For small involutive and integral quantaloids ${\cal Q}$ it is shown that covariant presheaves on symmetric ${\cal Q}$-categories are equivalent to certain subalgebras of a specific monad on the category of symmetric ${\cal Q}$-categories. This construction is related to a weakening of the subobject classifier axiom which does not require the classification of all subalgebras, but only guarantees that classifiable subalgebras are uniquely classifiable. As an application the identification of closed left ideals of non-commutative $C^*$-algebras with certain "open", subalgebras of freely generated algebras is given.
Publié le :
Classification : 06F07, 18C15, 18D20, 18F20
Keywords: Involutive quantale, involutive quantaloid, symmetric ${\cal Q}$-category, covariant presheaf, monad of weak singletons, classifiable subalgebra, closed left ideal 
@article{TAC_2011_25_a12,
     author = {Ulrich H\"ohle},
     title = {Covariant presheaves and subalgebras},
     journal = {Theory and applications of categories},
     pages = {342--367},
     publisher = {mathdoc},
     volume = {25},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2011_25_a12/}
}
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Ulrich Höhle. Covariant presheaves and subalgebras. Theory and applications of categories, Tome 25 (2011), pp. 342-367. http://geodesic.mathdoc.fr/item/TAC_2011_25_a12/