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- W3165579647 abstract "We provide a categorical interpretation for _escrows_, i.e. trading protocols in trustless environment, where the exchange between two agents is mediated by a third party where the buyer locks the money until they receive the goods they want from the seller. A simplified escrow system can be modeled as a certain kind of _optic_ in a monoidal category $mathcal M$ (e.g., the category of sets with cartesian product); escrows can be regarded as morphisms of a category $mathcal E(mathcal M)$, with the same objects of $mathcal M$, and where the hom-objects are $langle X , Y rangle = mathsf{Opt}_{mathcal M}(left[ begin{smallmatrix} Y X end{smallmatrix} right], left[ begin{smallmatrix} X Y end{smallmatrix} right])$. When $X$ is a comonoid and $Y$ is a monoid in $mathcal M$, $mathcal E(mathcal M)(X,Y)$ is a monoid in $mathsf{Set}$ (or in the base of enrichment chosen to model one's specific problem), acting on the set of optics $left[ begin{smallmatrix} B B end{smallmatrix} right] to left[ begin{smallmatrix} X Y end{smallmatrix} right]$. Moreover, we define a map $$lhd : langle Y , X rangle times mathsf{Opt}(left[ begin{smallmatrix} Y X end{smallmatrix} right], left[ begin{smallmatrix} B B end{smallmatrix} right]) to mathsf{Opt}(left[ begin{smallmatrix} Y X end{smallmatrix} right], left[ begin{smallmatrix}{Xotimes {Yotimes B} end{smallmatrix} right])$$ having action-like properties. This has the following interpretation: the object $B$ acts as an intermediary in a transaction between $X$ and $Y$, modeled by an escrow in $langle Y , X rangle$." @default.
- W3165579647 created "2021-06-07" @default.
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- W3165579647 date "2021-05-20" @default.
- W3165579647 modified "2023-09-27" @default.
- W3165579647 title "Escrows are optics" @default.
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