Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Bruguières, A., Lack, S., Virelizier, A.: Hopf monads on monoidal categories. Adv. Math. 227(2), 745–800 (2011)
Kelly, G.M.: Doctrinal adjunction. In: Kelly, G.M. (ed.) Category Seminar Sydney 1972/1973. Lecture Notes in Mathematics, vol. 420, pp. 257–280. Springer, Berlin (1974)
Mac Lane, S.: Categories for the Working Mathematician. Springer, Berlin (1978)
Street, R.: The formal theory of monads. J. Pure Appl. Algebra 2(2), 149–168 (1972)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Böhm, G. (2018). Lifting to Eilenberg–Moore Categories. In: Hopf Algebras and Their Generalizations from a Category Theoretical Point of View. Lecture Notes in Mathematics, vol 2226. Springer, Cham. https://doi.org/10.1007/978-3-319-98137-6_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-98137-6_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-98136-9
Online ISBN: 978-3-319-98137-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)