arXiv
Open Access
2020
Distributive laws for relative monads
Gabriele Lobbia
Abstrak
We introduce the notion of a distributive law between a relative monad and a monad. We call this a relative distributive law and define it in any 2-category $\mathcal{K}$. In order to do that, we introduce the 2-category of relative monads in a 2-category $\mathcal{K}$ with relative monad morphisms and relative monad transformations as 1- and 2-cells, respectively. We relate our definition to the 2-category of monads in $\mathcal{K}$ defined by Street. Thanks to this view we prove two Beck-type theorems regarding relative distributive laws. We also describe what does it mean to have Eilenberg-Moore and Kleisli objects in this context and give examples in the 2-category of locally small categories.
Topik & Kata Kunci
Penulis (1)
G
Gabriele Lobbia
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2020
- Bahasa
- en
- Sumber Database
- arXiv
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- Open Access ✓