--- tags: category theory, anders kock, monads --- $\newcommand{\sem}[1]{[\![#1]\!]}$ # Monoidal, Commutative and Double Dualization Monads As introduced by Anders Kock: ![](https://hackmd.io/_uploads/H1wgJwK2o.png) [4] refers to ![](https://hackmd.io/_uploads/S1WCJvF3j.png) [3] refers to ![](https://hackmd.io/_uploads/HkvlewYhi.png) See also the more recent ![](https://hackmd.io/_uploads/SkMBorSao.png) # References Anders Kock [homepage](https://users-math.au.dk/kock/) - Strong functors and monoidal monads Arch.Math. (Basel) 23 (1972), 113-120. http://tildeweb.au.dk/au76680/SFMM.pdf - On double dualization monads, Math. Scand. 27 (1970), 151-165. http://tildeweb.au.dk/au76680/DD.pdf - Closed categories generated by commutative monads, J. Austral. Math. Soc. 12 (1971), 405-424. http://tildeweb.au.dk/au76680/CCGBCM.pdf - Monads on symmetric monoidal closed categories, Archiv.Math. (Basel) 21 (1970), 1-9. http://tildeweb.au.dk/au76680/MSMCC.pdf - Commutative monads as a theory of distributions. Theory and Applications of Categories, Vol. 26, 2012, No. 4, pp 97-131. http://www.tac.mta.ca/tac/volumes/26/4/26-04.pdf Further References: - Francois Metayer [State monads and their algebras](https://arxiv.org/pdf/math/0407251.pdf) - Marcelo Fiore, [An Equational Metalogic for Monadic Equational Systems](https://arxiv.org/abs/1309.4821), 2013. - Mathoverflow: [What are the algebras for the double dualization monad?](https://mathoverflow.net/questions/104777/what-are-the-algebras-for-the-double-dualization-monad), 2004