Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Concept

Monad (category theory)

Related publications (17)

Homotopical relations between 2-dimensional categories and their infinity-analogues

Lyne Moser

In this thesis, we study the homotopical relations of 2-categories, double categories, and their infinity-analogues. For this, we construct homotopy theories for the objects of interest, and show that there are homotopically full embeddings of 2-categories ...

EPFL2021

Twisting structures and morphisms up to strong homotopy

Kathryn Hess Bellwald

We define twisted composition products of symmetric sequences via classifying morphisms rather than twisting cochains. Our approach allows us to establish an adjunction that simultaneously generalizes a classic one for algebras and coalgebras, and the bar- ...

2020

The Homotopy Theory Of Coalgebras Over Simplicial Comonads

Kathryn Hess Bellwald, Magdalena Kedziorek

We apply the Acyclicity Theorem of Hess, Kedziorek, Riehl, and Shipley (recently corrected by Garner, Kedziorek, and Riehl) to establishing the existence of model category structure on categories of coalgebras over comonads arising from simplicial adjuncti ...

INT PRESS BOSTON, INC2019

Towards an (∞,2)-category of homotopy coherent monads in an ∞-cosmos

Dimitri Zaganidis

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 ...

EPFL2017

A necessary and sufficient condition for induced model structures

Kathryn Hess Bellwald, Magdalena Kedziorek

A common technique for producing a new model category structure is to lift the fibrations and weak equivalences of an existing model structure along a right adjoint. Formally dual but technically much harder is to lift the cofibrations and weak equivalence ...

Wiley2017

Exponential Kleisli Monoids as Eilenberg-Moore Algebras

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

Left-induced model structures and diagram categories

Kathryn Hess Bellwald, Magdalena Kedziorek, Varvara Karpova

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 ...

2015

The renormalon diagram in gauge theories on R-3 x S-1

We analyze the renormalon diagram of gauge theories on . In particular, we perform exact one loop calculations for the vacuum polarization in QCD with adjoint matter and observe that all infrared logarithms, as functions of the external momentum, cancel be ...

Springer Nature2015

The homotopy theory of coalgebras over a comonad

Kathryn Hess Bellwald

Let K be a comonad on a model category M. We provide conditions under which the associated category of K-coalgebras admits a model category structure such that the forgetful functor to M creates both cofibrations and weak equivalences. We provide concrete ...

2014

Tensors, Monads And Actions

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

Order-adjoint monads and injective objects

Given a monad T on Set whose functor factors through the category of ordered sets with left adjoint maps, the category of Kleisli monoids is defined as the category of monoids in the hom-sets of the Kleisli category of T. The Eilenberg-Moore category of T ...

Elsevier2010

Bar constructions and Quillen homology of modules over operads

We show that topological Quillen homology of algebras and modules over operads in symmetric spectra can be calculated by realizations of simplicial bar constructions. Working with several model category structures, we give a homotopical proof after showing ...

2010

Model-Based Estimation of Three-Dimensional Stiffness Parameters in Photonic-Force Microscopy

Michaël Unser, Andrzej Kulik, Philippe Thévenaz, Elena Bertseva

We propose a system to characterize the 3-D diffusion properties of the probing bead trapped by a photonic-force microscope. We follow a model-based approach, where the model of the dynamics of the bead is given by the Langevin equation. Our procedure comb ...

Institute of Electrical and Electronics Engineers2010

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

Related publications (17)

G

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

2009