Concept

Monad (category theory)

Related publications (26)

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

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- ...

2019

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

Genome-wide variation in nucleotides and retrotransposons in alpine populations of Arabis alpina (Brassicaceae)

Stéphane Joost, Aude Rogivue

Advances in high‐throughput sequencing have promoted the collection of reference genomes and genome‐wide diversity. However, the assessment of genomic variation among populations has hitherto mainly been surveyed through single‐nucleotide polymorphisms (SN ...

2019

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

Simplicitly: Foundations and Applications of Implicit Function Types

Martin Odersky, Fengyun Liu, Sandro Stucki, Olivier Eric Paul Blanvillain

Understanding a program entails understanding its context; dependencies, configurations and even implementations are all forms of contexts. Modern programming languages and theorem provers offer an array of constructs to define contexts, implicitly. Scala ...

2017

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

Left-induced model structures and diagram categories

Kathryn Hess Bellwald, Varvara Karpova, Magdalena Kedziorek

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

Left-Induced Model Structures and Diagram Categories

Kathryn Hess Bellwald, Varvara Karpova, Magdalena Kedziorek

We prove existence results a 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 ...

Amer Mathematical Soc2015

Graph Chatbot

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.