# Homology and cohomology via enriched bifunctors

@article{Shimakawa2010HomologyAC, title={Homology and cohomology via enriched bifunctors}, author={Kazuhisa Shimakawa and Ken'ichi Yoshida and Tadayuki Haraguchi}, journal={arXiv: Algebraic Topology}, year={2010} }

We show that the category of numerically generated pointed spaces is complete, cocomplete, and monoidally closed with respect to the smash product, and then utilize these features to establish a simple but flexible method for constructing generalized homology and cohomology theories by using the notion of enriched bifunctors.

## 24 Citations

STEENROD-ČECH HOMOLOGY-COHOMOLOGY THEORIES ASSOCIATED WITH BIVARIANT FUNCTORS

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Let NG0 denote the category of all pointed numerically generated spaces and continuous maps preserving base-points. In [SYH], we described a passage from bivariant functors NG 0 ×NG0 → NG0 to…

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Let P be a poset. In this note we define a combinatorial simplicial model structure on the category of simplicial sets over the nerve of P whose underlying ∞category is the∞-category of P-stratified…

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By using local systems over simplicial sets with values in differential graded algebras, we consider a framework of rational and R-local homotopy theory for diffeological spaces with arbitrary…

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In this paper we present the notion of de Rham cohomology with compact support for diffeological spaces.
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Stratifolds are considered from a categorical point of view. We show among others that the category of stratifolds fully faithfully embeds into the category of ${\mathbb R}$-algebras as does the…

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Let $P$ be a poset. In this note we define a combinatorial simplicial model structure on the category of simplicial sets over the nerve of $P$ whose underlying $\infty$-category is the…

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STEENROD-ČECH HOMOLOGY-COHOMOLOGY THEORIES ASSOCIATED WITH BIVARIANT FUNCTORS

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Let NG0 denote the category of all pointed numerically generated spaces and continuous maps preserving base-points. In [SYH], we described a passage from bivariant functors NG 0 ×NG0 → NG0 to…

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