6 papers
Realification of stably trivial vector bundles
Guy Boyde, Niall Taggart
The set of stably trivial complex vector bundles over complex projective spaces and spheres has a natural group structure when the corank is small enough. With respect to this grou…
Deconstructing span categories for profinite groups
David Barnes, Niall Taggart
One of the major advantages of -category theory over classical -category theory is its robust and homotopically meaningful framework for taking (co)limits of diagrams of…
A Dwyer-Rezk classification for polynomial functors in Weiss calculus
David Barnes, Magdalena KÄdziorek, Niall Taggart
In Goodwillie calculus, unpublished work of Dwyer and Rezk provides a classification of reduced filtered colimit preserving -excisive functors from pointed spaces to spectra as…
An algebraic model for rational excisive functors
David Barnes, Magdalena KÄdziorek, Niall Taggart
We provide a new proof of the rational splitting of excisive endofunctors of spectra as a product of their homogeneous layers independent of rational Tate vanishing. We utilise the…
Symplectic Weiss calculi
Matthew Carr, Niall Taggart
We provide two candidates for symplectic Weiss calculus based on two different, but closely related, collections of groups. In the case of the non-compact symplectic groups, i.e.,…
Koszul duality and a classification of stable Weiss towers
Connor Malin, Niall Taggart
We introduce a version of Koszul duality for categories, which extends the Koszul duality of operads and right modules. We demonstrate that the derivatives which appear in Weiss ca…