1. The formal theory of monoidal monads
- Author
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Zawadowski, Marek
- Subjects
- *
MONOIDS , *MONADS (Mathematics) , *MORPHISMS (Mathematics) , *CATEGORIES (Mathematics) , *MATHEMATICAL analysis , *ISOMORPHISM (Mathematics) - Abstract
Abstract: We give a 3-categorical, purely formal argument explaining why on the category of Kleisli algebras for a lax monoidal monad, and dually on the category of Eilenberg–Moore algebras for an oplax monoidal monad, we always have a natural monoidal structures. The key observation is that the 2-category of lax monoidal monads in any 2-category D with finite products is isomorphic to the 2-category of monoidal objects with oplax morphisms in the 2-category of monads with lax morphisms in D. We explain at the end of the paper that a similar phenomenon occurs in many other situations. [Copyright &y& Elsevier]
- Published
- 2012
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