7 papers · 1 filter
On tested Bousfield-Friedlander localizations
Niall Taggart
We demonstrate that a Bousfield-Friedlander localization with a set of test morphisms in the sense introduced by Bandklayder, Bergner, Griffiths, Johnson, and Santhanam can also be…
Comparing orthogonal calculus and calculus with Reality
Niall Taggart
We show that there exists a suitable -fixed points functor from calculus with Reality to the orthogonal calculus of Weiss which recovers orthogonal calculus ``up to a shift''…
The localization of orthogonal calculus with respect to homology
Niall Taggart
For a set of maps of based spaces we construct a version of Weiss' orthogonal calculus which depends only on the -local homotopy type of the functor involved. We show that $…
Recovering unitary calculus from calculus with reality
Niall Taggart
By analogy with complex --theory and --theory with reality, there are theories of unitary functor calculus and unitary functor calculus with reality, both of which are genera…
Unitary Functor Calculus with Reality
Niall Taggart
We construct a calculus of functors in the spirit of orthogonal calculus, which is designed to study "functors with reality" such as the Real classifying space functor, $BU_\mathbb…
Comparing the orthogonal and unitary functor calculi
Niall Taggart
The orthogonal and unitary calculi give a method to study functors from the category of real or complex inner product spaces to the category of based topological spaces. We constru…