منابع مشابه
Galois Theory of Simplicial Complexes
We examine basic notions of categorical Galois theory for the adjunction between Π0 and the inclusion as discrete, in the case of simplicial complexes. Covering morphisms are characterized as the morphisms satisfying the unique simplex lifting property, and are classified by means of the fundamental groupoid, for which we give an explicit “Galoistheoretic” description. The class of covering mor...
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We recall and reformulate certain known constructions, in order to make a convenient setting for obtaining generalized monotone-light factorizations in the sense of A. Carboni, G. Janelidze, G. M. Kelly and R. Paré. This setting is used to study the existence of monotone-light factorizations both in categories of simplicial objects and in categories of internal categories. It is shown that ther...
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Towards a Spectral Theory for Simplicial Complexes
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A clutter $mathcal{C}$ with vertex set $[n]$ is an antichain of subsets of $[n]$, called circuits, covering all vertices. The clutter is $d$-uniform if all of its circuits have the same cardinality $d$. If $mathbb{K}$ is a field, then there is a one-to-one correspondence between clutters on $V$ and square-free monomial ideals in $mathbb{K}[x_1,ldots,x_n]$ as follows: To each clutter $mathcal{C}...
متن کاملMinors of simplicial complexes
We extend the notion of a minor from matroids to simplicial complexes. We show that the class of matroids, as well as the class of independence complexes, is characterized by a single forbidden minor. Inspired by a recent result of Aharoni and Berger, we investigate possible ways to extend the matroid intersection theorem to simplicial complexes.
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2003
ISSN: 0166-8641
DOI: 10.1016/s0166-8641(03)00036-1