Work

The six operations in topology

Year: 2025

Type: article

Abstract: In this paper, we show that the six functor formalism for sheaves on locally compact Hausdorff topological spaces, as developed, for example,‐ in Kashiwara and Schapira's book Sheaves on Manifolds , can be extended to sheaves with values in any closed symmetric monoidal ‐category which is stable and bicomplete. Notice that, since we do not assume that our coefficients are presentable or restrict to hypercomplete sheaves, our arguments are not obvious and are substantially different from the ones explained by Kashiwara and Schapira. Along the way we also study locally contractible geometric morphisms and prove that, if is a continuous map which induces a locally contractible geometric morphism, then the exceptional pullback functor preserves colimits and can be related to the pullback . At the end of our paper, we also show how one can express Atiyah duality by means of the six functor formalism.

Source: Journal of Topology

DOI: 10.1112/topo.70050

Author: Marco Volpe

Institution: University of Regensburg

Language: English

Topic: Homotopy and Cohomology in Algebraic Topology

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: Deutsche Forschungsgemeinschaft