A symmetric monoidal Comparison Lemma
| Autor: | Kuijper, Josefien |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this note we study symmetric monoidal functors from a symmetric monoidal 1-category to a cartesian symmetric monoidal $\infty$-category, which are in addition hypersheaves for a certain topology. We prove a symmetric monoidal version of the Comparison Lemma, for lax as well as strong symmetric monoidal hypersheaves. For a strong symmetric monoidal functor between symmetric monoidal 1-categories with topologies generated by suitable cd-structures, we show that if the conditions of the Comparison Lemma are satisfied, then there is also an equivalence between categories of lax and strong symmetric monoidal hypersheaves respectively, taking values in a complete cartesian symmetric monoidal $\infty$-category. As an application of this result, we prove a lax symmetric monoidal version of our previous result about hypersheaves that encode compactly supported cohomology theories. Comment: This note is now superseded by Section 4.2 of 2309.11449v3 |
| Databáze: | arXiv |
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