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arXiv · 2209.05908

Monoidal Pull-Push II: Local Systems

Angus Hadrian Rush
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Abstract

Our aim in this work is to provide an explicit, simple construction of pull-push of local systems as a lax monoidal functor. To this end, we show that one can solve horn filling problems Cat_\infty using left Kan extensions, and use this to provide an explicit construction of a left Kan extension functor. We use this result to show that pull-push of local systems induces a functor from Span(S), the infinity category of spans of spaces, into Cat_\infty. We then develop a machinery of monoidal Beck-Chevalley fibrations, and use this to show that the pull-push functor above admits a lax monoidal structure.

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Angus Hadrian Rush. 2022-09-13. Monoidal Pull-Push II: Local Systems. https://arxiv.org/abs/2209.05908

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