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Ben Sprott
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In this post, I was introduced to the monad of finitely supported measures.

$HX$ is the set of finitely supported measures on $X$, with monad structure defined as for the Giry monad.

I have three questions. This monad, $H$, is presented on Set in the post, but I am wondering if the category of groupoids supports this monad? What is the category of factorizations of this monad on Set and what is the category of factorizations of this monad on the category of groupoids? A factorization of a monad $M$ on category $C$ is a category $D$, and an adjunction $U,V$ between $C$ and $D$ that generates the monad $M$. What is the KleisliEilenberg-Moore category for this monad on the category of groupoids?

In this post, I was introduced to the monad of finitely supported measures.

$HX$ is the set of finitely supported measures on $X$, with monad structure defined as for the Giry monad.

I have three questions. This monad, $H$, is presented on Set in the post, but I am wondering if the category of groupoids supports this monad? What is the category of factorizations of this monad on Set and what is the category of factorizations of this monad on the category of groupoids? A factorization of a monad $M$ on category $C$ is a category $D$, and an adjunction $U,V$ between $C$ and $D$ that generates the monad $M$. What is the Kleisli category for this monad on the category of groupoids?

In this post, I was introduced to the monad of finitely supported measures.

$HX$ is the set of finitely supported measures on $X$, with monad structure defined as for the Giry monad.

I have three questions. This monad, $H$, is presented on Set in the post, but I am wondering if the category of groupoids supports this monad? What is the category of factorizations of this monad on Set and what is the category of factorizations of this monad on the category of groupoids? A factorization of a monad $M$ on category $C$ is a category $D$, and an adjunction $U,V$ between $C$ and $D$ that generates the monad $M$. What is the Eilenberg-Moore category for this monad on the category of groupoids?

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Ben Sprott
  • 1.3k
  • 14
  • 23

In this post, I was introduced to the monad of finitely supported measures.

$HX$ is the set of finitely supported measures on $X$, with monad structure defined as for the Giry monad.

I have twothree questions. This monad, $H$, is presented on Set in the post, but I am wondering if the category of groupoids supports this monad? What is the category of factorizations of this monad on Set and what is the category of factorizations of this monad on the category of groupoids? A factorization of a monad $M$ on category $C$ is a category $D$, and an adjunction $U,V$ between $C$ and $D$ that generates the monad $M$. What is the Kleisli category for this monad on the category of groupoids?

In this post, I was introduced to the monad of finitely supported measures.

$HX$ is the set of finitely supported measures on $X$, with monad structure defined as for the Giry monad.

I have two questions. This monad, $H$, is presented on Set in the post, but I am wondering if the category of groupoids supports this monad? What is the category of factorizations of this monad on Set and what is the category of factorizations of this monad on the category of groupoids? A factorization of a monad $M$ on category $C$ is a category $D$, and an adjunction $U,V$ between $C$ and $D$ that generates the monad $M$. What is the Kleisli category for this monad on the category of groupoids?

In this post, I was introduced to the monad of finitely supported measures.

$HX$ is the set of finitely supported measures on $X$, with monad structure defined as for the Giry monad.

I have three questions. This monad, $H$, is presented on Set in the post, but I am wondering if the category of groupoids supports this monad? What is the category of factorizations of this monad on Set and what is the category of factorizations of this monad on the category of groupoids? A factorization of a monad $M$ on category $C$ is a category $D$, and an adjunction $U,V$ between $C$ and $D$ that generates the monad $M$. What is the Kleisli category for this monad on the category of groupoids?

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Ben Sprott
  • 1.3k
  • 14
  • 23

What is the category of algebras for the finitely supported measures monad?

In this post, I was introduced to the monad of finitely supported measures.

$HX$ is the set of finitely supported measures on $X$, with monad structure defined as for the Giry monad.

I have two questions. This monad, $H$, is presented on Set in the post, but I am wondering if the category of groupoids supports this monad? What is the category of factorizations of this monad on Set and what is the category of factorizations of this monad on the category of groupoids? A factorization of a monad $M$ on category $C$ is a category $D$, and an adjunction $U,V$ between $C$ and $D$ that generates the monad $M$. What is the Kleisli category for this monad on the category of groupoids?