Following Eilenberg-Steenrod axiomatic approach we construct the universal ordinary homology theory for any homological structure on a given category by representing ordinary theories with values in abelian categories. For a convenient category of spaces we then obtain a universal abelian category which can be actually described for CW-complexes as the category of hieratic modules.

On topological motives / L. BARBIERI VIALE. - In: TOPOLOGY AND ITS APPLICATIONS. - ISSN 0166-8641. - 314:(2022 Jun 01), pp. 108141.1-108141.23. [10.1016/j.topol.2022.108141]

### On topological motives

#### Abstract

Following Eilenberg-Steenrod axiomatic approach we construct the universal ordinary homology theory for any homological structure on a given category by representing ordinary theories with values in abelian categories. For a convenient category of spaces we then obtain a universal abelian category which can be actually described for CW-complexes as the category of hieratic modules.
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Mathematics; Algebraic Geometry; Mathematics; Algebraic Topology; Mathematics; Category Theory; Mathematics; K-Theory and Homology;
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/930351`