### Combinatorial homology in a perspective of image analysis.

Grandis, Marco (2003)

Georgian Mathematical Journal

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Grandis, Marco (2003)

Georgian Mathematical Journal

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Jaroslav Guričan (1993)

Commentationes Mathematicae Universitatis Carolinae

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The isomorphism between our homology functor and these of Vietoris and Čech is proved. Introductory result on dimension is proved.

Marek Filakovský (2014)

Archivum Mathematicum

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We extend the notion of simplicial set with effective homology presented in [22] to diagrams of simplicial sets. Further, for a given finite diagram of simplicial sets $X:\mathcal{I}\to \text{sSet}$ such that each simplicial set $X\left(i\right)$ has effective homology, we present an algorithm computing the homotopy colimit $\text{hocolim}\phantom{\rule{0.166667em}{0ex}}X$ as a simplicial set with effective homology. We also give an algorithm computing the cofibrant replacement ${X}^{\text{cof}}$ of $X$ as a diagram with effective homology. This is applied to computing of equivariant cohomology...

Su-Cheng Chang (1966)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Steven Garavaglia (1978)

Fundamenta Mathematicae

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