Concept

Cartesian monoidal category

Publications associées (9)

Rational SO(2)- equivariant spectra

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 ...

Geometry & Topology Publications2017

Waldhausen K-theory of spaces via comodules

Kathryn Hess Bellwald

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 ...

Academic Press Inc Elsevier Science2016

Exponential Kleisli Monoids as Eilenberg-Moore Algebras

Gavin Jay Seal, Dirk Hofmann

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 ...

Springer2015

Tensors, Monads And Actions

Gavin Jay Seal

We exhibit sufficient conditions for a monoidal monad T on a monoidal category C to induce a monoidal structure on the Eilenberg-Moore category C^T that represents bimorphisms. The category of actions in C^T is then shown to be monadic over the base catego ...

Mount Allison University2013

Normal and conormal maps in homotopy theory

Kathryn Hess Bellwald

Let M be a monoidal category endowed with a distinguished class of weak equivalences and with appropriately compatible classifying bundles for monoids and comonoids. We define and study homotopy-invariant notions of normality for maps of monoids and of con ...

Int Press Boston, Inc2012

Homotopic Descent over Monoidal Model Categories

The starting point for this project is the article of Kathryn Hess [11]. In this article, a homotopic version of monadic descent is developed. In the classical setting, one constructs a category D(𝕋) of coalgebras in the Eilenberg-Moore category of ...

EPFL2011

Categorical Foundations for K-theory

Nicolas Mathieu Michel

K-Theory was originally defined by Grothendieck as a contravariant functor from a subcategory of schemes to abelian groups, known today as K0. The same kind of construction was then applied to other fields of mathematics, like spaces and (not necessarily c ...

EPFL2010

Homotopic Hopf-Galois extensions: foundations and examples

Kathryn Hess Bellwald

Hopf-Galois extensions of rings generalize Galois extensions, with the coaction of a Hopf algebra replacing the action of a group. Galois extensions with respect to a group

G

are the Hopf-Galois extensions with respect to the dual of the group algebra of ...

2009

Coalgèbres d'Alexander-Whitney : un modèle algébrique pour les espaces topologiques

Théophile Naïto

The goal of this work is to study Alexander-Whitney coalgebras (first defined in [HPST06]) from a topological point of view. An Alexander-Whitney coalgebra is a coassociative chain coalgebra over Z with an extra algebraic structure : the comultiplication m ...

EPFL2009

Homotopic Hopf-Galois extensions: foundations and examples

Kathryn Hess Bellwald

Hopf-Galois extensions of rings generalize Galois extensions, with the coaction of a Hopf algebra replacing the action of a group. Galois extensions with respect to a group

G

are the Hopf-Galois extensions with respect to the dual of the group algebra of ...

2009