Lifting to Eilenberg–Moore categories

Research output: Chapter in Book/Report/Conference proceedingChapter


This chapter is used to present the necessary background on category theory. The structures occurring in the later sections are introduced and their key properties are discussed. All of the definitions are illustrated by collections of examples, chosen by their relevance in the applications in the later sections. First some basic notions such as category, functor and natural transformation are defined and operations with them are explained. This allows for the introduction of adjunctions and monads. The Eilenberg–Moore category of a monad is defined together with the key concept of lifting of functors, natural transformations and adjunctions to Eilenberg–Moore categories of monads.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Number of pages22
Publication statusPublished - Jan 1 2018

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434


ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Böhm, G. (2018). Lifting to Eilenberg–Moore categories. In Lecture Notes in Mathematics (pp. 7-28). (Lecture Notes in Mathematics; Vol. 2226). Springer Verlag.