| Autor: |
Adámek, J., Dostál, M., Velebil, J. |
| Rok vydání: |
2020 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
It is well known that classical varieties of $\Sigma$-algebras correspond bijectively to finitary monads on $\mathsf{Set}$. We present an analogous result for varieties of ordered $\Sigma$-algebras, i.e., classes presented by inequations between $\Sigma$-terms. We prove that they correspond bijectively to strongly finitary monads on $\mathsf{Pos}$. That is, those finitary monads which preserve reflexive coinserters. We deduce that strongly finitary monads have a coinserter presentation, analogous to the coequaliser presentation of finitary monads due to Kelly and Power. We also show that these monads are liftings of finitary monads on $\mathsf{Set}$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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