Parametrized and equivariant higher algebra
D Nardin, J Shah - arXiv preprint arXiv:2203.00072, 2022 - arxiv.org
We develop the rudiments of a theory of parametrized $\infty $-operads, including
parametrized generalizations of monoidal envelopes, Day convolution, operadic left Kan …
parametrized generalizations of monoidal envelopes, Day convolution, operadic left Kan …
Twisted ambidexterity in equivariant homotopy theory
B Cnossen - arXiv preprint arXiv:2303.00736, 2023 - arxiv.org
We develop the concept of twisted ambidexterity in a parametrized presentably symmetric
monoidal $\infty $-category, which generalizes the notion of ambidexterity by Hopkins and …
monoidal $\infty $-category, which generalizes the notion of ambidexterity by Hopkins and …
[HTML][HTML] Parametrised presentability over orbital categories
K Hilman - Applied Categorical Structures, 2024 - Springer
In this paper, we develop the notion of presentability in the parametrised homotopy theory
framework of Barwick et al.(Parametrized higher category theory and higher algebra: a …
framework of Barwick et al.(Parametrized higher category theory and higher algebra: a …
Parametrised noncommutative motives and equivariant cubical descent in algebraic K-theory
K Hilman - arXiv preprint arXiv:2202.02591, 2022 - arxiv.org
For an atomic orbital base category in the sense of Barwick-Dotto-Glasman-Nardin-Shah,
we introduce the category of parametrised perfect-stable categories and use it to construct …
we introduce the category of parametrised perfect-stable categories and use it to construct …
Tate blueshift and vanishing for real oriented cohomology theories
G Li, V Lorman, JD Quigley - Advances in Mathematics, 2022 - Elsevier
We study transchromatic phenomena for the Tate construction of Real oriented cohomology
theories. First, we show that after suitable completion, the Tate construction with respect to a …
theories. First, we show that after suitable completion, the Tate construction with respect to a …
Parametrized higher semiadditivity and the universality of spans
B Cnossen, T Lenz, S Linskens - arXiv preprint arXiv:2403.07676, 2024 - arxiv.org
Using the framework of ambidexterity developed by Hopkins and Lurie, we introduce a
parametrized analogue of higher semiadditivity called $\mathcal Q $-semiadditivity …
parametrized analogue of higher semiadditivity called $\mathcal Q $-semiadditivity …
The Adams isomorphism revisited
B Cnossen, T Lenz, S Linskens - arXiv preprint arXiv:2311.04884, 2023 - arxiv.org
We establish abstract Adams isomorphisms in an arbitrary equivariantly presentable
equivariantly semiadditive global category. This encompasses the well-known Adams …
equivariantly semiadditive global category. This encompasses the well-known Adams …
Tate blueshift and vanishing for Real oriented cohomology
G Li, V Lorman, JD Quigley - arXiv preprint arXiv:1910.06191, 2019 - arxiv.org
We study transchromatic phenomena for the Tate construction of Real oriented cohomology
theories. First, we show that after suitable completion, the Tate construction with respect to a …
theories. First, we show that after suitable completion, the Tate construction with respect to a …
An Equivariant Generalisation of McDuff–Segal's Group–Completion Theorem
K Hilman - International Mathematics Research Notices, 2024 - academic.oup.com
In this short note, we prove a–equivariant generalisation of McDuff–Segal's group–
completion theorem for finite groups. A new complication regarding genuine equivariant …
completion theorem for finite groups. A new complication regarding genuine equivariant …