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We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties wh ...
We prove that the category of rational SO(2)-equivariant spectra has a simple algebraic model. Furthermore, all of our model categories and Quillen equivalences are monoidal, so we can use this classification to understand ring spectra and module spectra v ...
This thesis is part of a program initiated by Riehl and Verity to study the category theory of (infinity,1)-categories in a model-independent way. They showed that most models of (infinity,1)-categories form an infinity-cosmos K, which is essentially a cat ...
We present and discuss current waveforms associated with 13 bipolar lightning flashes recorded at the Santis Tower during the period from June 2010 to January 2015. During this period, a total of 427 flashes were recorded, of which 13 (3%) were classified ...
Kan spectra provide a combinatorial model for the stable homotopy category. They were introduced by Dan Kan in 1963 under the name semisimplicial spectra. A Kan spectrum is similar to a pointed simplicial set, but it has simplices in negative degrees as we ...
We prove existence results à la Jeff Smith for left-induced model category structures, of which the injective model structure on a diagram category is an important example. We further develop the notions of fibrant generation and Postnikov presentation fro ...
We compute the L-2-Betti numbers of the free C*-tensor categories, which are the representation categories of the universal unitary quantum groups A(u)(F). We show that the L-2-Betti numbers of the dual of a compact quantum group G are equal to the L-2-Bet ...
Let X be a simplicial set. We construct a novel adjunction be- tween the categories RX of retractive spaces over X and ComodX+ of X+- comodules, then apply recent work on left-induced model category structures [5], [16] to establish the existence of a left ...
Let G be a finite group and R be a commutative ring. The Mackey algebra μR(G) shares a lot of properties with the group algebra RG however, there are some differences. For example, the group algebra is a symmetric algebra and this is not always the case fo ...
Lax monoidal powerset-enriched monads yield a monoidal structure on the category of monoids in the Kleisli category of a monad. Exponentiable objects in this category are identified as those Kleisli monoids with algebraic structure. This result generalizes ...
