hadriah

• Heine, Hadrian Ernst Hermann (2026). A local-global principle for parametrized -categories. Forum of Mathematics, Sigma. 14. doi: 10.1017/fms.2025.10155. Full text in Research Archive Show summary

  We prove a local-global principle for parametrized ∞-categories: we show that any functor B →C is determined by the following data: the collection of fibers B𝑋 for X running through the set of equivalence classes of objects of C endowed with the action of the space of automorphisms Aut𝑋⁢(B) on the fiber, the local data, together with a locally cartesian fibration D →C and Aut𝑋⁢(B)-linear equivalences D𝑋 ≃P⁡(B𝑋) to the ∞-category of presheaves on B𝑋, the gluing data. As applications we compute the mapping spaces of the conditionally existing internal hom of ∞⁢Cat/C and extend the ∞-categorical Grothendieck-construction by proving that ∞-categories over any ∞-category C are classified by normal lax 2-functors to a double ∞-category of correspondences.

• Heine, Hadrian Ernst Hermann (2025). A topological model for cellular motivic spectra. Israel Journal of Mathematics. ISSN 0021-2172. doi: 10.1007/s11856-025-2836-9. Full text in Research Archive Show summary

  For any motivic E∞-ring spectrum A we construct an equivalence ρ between the ∞-category of cellular motivic A-module spectra and modules over an E1-algebra Θ in Z-graded spectra, under which the motivic grading corresponds to the Z-grading. If the base is C or if A admits an E∞-orientation, we refine the E1-algebra Θ to an E∞-algebra and ρ to a symmetric monoidal equivalence. To capture the symmetric monoidal structure in the general situation, we lift ρ to a symmetric monoidal equivalence to modules over an E∞ algebra in J-graded spectra that invert morphisms of J,whereJ is the diagram category of Sagave–Schlichtkrull [15], a model for Quillen’s localization of the groupoid of finite sets and bijections

• Heine, Hadrian Ernst Hermann (2025). An Equivalence Between Two Models of ∞-Categories of Enriched Presheaves. Applied Categorical Structures. ISSN 0927-2852. 33. doi: 10.1007/s10485-024-09792-x. Full text in Research Archive
• Heine, Hadrian Ernst Hermann (2023). An equivalence between enriched ∞-categories and ∞-categories with weak action. Advances in Mathematics. ISSN 0001-8708. 417. doi: 10.1016/j.aim.2023.108941. Full text in Research Archive

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• Heine, Hadrian Ernst Hermann (2024). Restricted L_infinity-algebras and a derived Milnor-Moore theorem. arXiv. Full text in Research Archive
• Heine, Hadrian Ernst Hermann (2024). The higher algebra of weighted colimits. arXiv. Full text in Research Archive
• Heine, Hadrian Ernst Hermann (2024). On bi-enriched infinity-categories. arXiv. Full text in Research Archive
• Heine, Hadrian Ernst Hermann (2024). A local-global principle for parametrized infinity-categories. arXiv. Full text in Research Archive
• Heine, Hadrian Ernst Hermann (2023). An equivalence between two models of infinity-categories of enriched presheaves. arXiv. Full text in Research Archive
• Heine, Hadrian Ernst Hermann; Spitzweck, Markus & Verdugo, Paula (2021). Real K-theory for Waldhausen infinity categories with genuine duality. arXiv. Full text in Research Archive
• Heine, Hadrian Ernst Hermann; Spitzweck, Markus & Lopez-Avila, Alejo (2020). Infinity categories with duality and hermitian multiplicative infinite loop space machines. arXiv. Full text in Research Archive
• Heine, Hadrian Ernst Hermann (2018). A monadicity theorem for higher algebraic structures. arXiv. Full text in Research Archive
• Heine, Hadrian Ernst Hermann (2017). A topological model for cellular motivic spectra. arXiv. Full text in Research Archive

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