Sweedler Theory of Monads-Reference-Cited by-同舟云学术

Sweedler Theory of Monads

Published:2022 Issue: Volume: Page:428-448
ISSN:0302-9743
Container-title:Lecture Notes in Computer Science
language:
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Author:

McDermott Dylan^ORCID,Rivas Exequiel^ORCID,Uustalu Tarmo^ORCID

Abstract

AbstractMonad-comonad interaction laws are a mathematical concept for describing communication protocols between effectful computations and coeffectful environments in the paradigm where notions of effectful computation are modelled by monads and notions of coeffectful environment by comonads. We show that monad-comonad interaction laws are an instance of measuring maps from Sweedler theory for duoidal categories whereby the final interacting comonad for a monad and a residual monad arises as the Sweedler hom and the initial residual monad for a monad and an interacting comonad as the Sweedler copower. We then combine this with a (co)algebraic characterization of monad-comonad interaction laws to derive descriptions of the Sweedler hom and the Sweedler copower in terms of their coalgebras resp. algebras.

Publisher

Springer International Publishing

Link

https://link.springer.com/content/pdf/10.1007/978-3-030-99253-8_22

Reference34 articles.

1. Adámek, J., Rosický, J.: Locally Presentable and Accessible Categories, London Math. Soc. Lecture Note Series, vol. 189. Cambridge University Press (1994)

2. Aguiar, M., Mahajan, S.: Monoidal Functors, Species and Hopf Algebras, CRM Monograph Series, vol. 29. Amer. Math. Soc. (2010)

3. Anel, M., Joyal, A.: Sweedler theory of (co)algebras and the bar-cobar construction. arXiv eprint 1309.6952 [math.CT] (2013), https://arxiv.org/abs/1309.6952

4. Bergman, G.M.: An Invitation to General Algebra and Universal Constructions. Universitext, Springer (2015). https://doi.org/10.1007/978-3-319-11478-1, author’s revised version at https://math.berkeley.edu/~gbergman/245/

5. Bergman, G.M., Hausknecht, A.O.: Cogroups and Co-rings in Categories of Associative Rings, AMS Mathematical Surveys and Monographs, vol. 45. Amer. Math. Soc. (1996)