The formal theory of monoidal monads
| Autor: | Marek Zawadowski |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Higher category theory
Algebra and Number Theory Theory Mathematics - Category Theory Symmetric monoidal category Closed monoidal category Algebra Morphism Computer Science::Logic in Computer Science Mathematics::Category Theory FOS: Mathematics Monoidal monad Category Theory (math.CT) Argument (linguistics) Enriched category Mathematics |
| Zdroj: | Journal of Pure and Applied Algebra. 216:1932-1942 |
| ISSN: | 0022-4049 |
| DOI: | 10.1016/j.jpaa.2012.02.030 |
| Popis: | 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. As we explain at the end of the paper a similar phenomenon occurs in many other situations. Comment: 15 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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