### 7 What is the polynomial functor for the Bag monad

I may be wrong, but we should be able to write the Bag monad in a polynomial form. The bag monad, is exectly the multiset monad whose category of algebras are the commutative monoids. Another name ...

### 25 Why are monadicity and descent related?

This question is probably too vague for experts, but I really don't know how to avoid it. I've read in several places that under mild conditions, a morphism is an effective descent morphism iff the ...

### 1 Monads associated to Higher Categories

By Koudenburg The paper (arXiv:[1511.04070])(https://arxiv.org/pdf/1511.04070) generalizes 2-monad associated to hyper virtual double category. Another paper (arXiv:[1310.8279]) (https://arxiv.org/...

### 2 Is this Frobenius Monad left exact? Does it preserve equalizers?

In this paper we see a Frobenius Monad in example 5.2. Suppose we take Hilb as the underlying category. Is this functor left exact? Does it preserve equalizers?

### 1 Synthetic type theory for virtual double category and its higher categories

For some monad T on a virtual equipment, the paper A unified framework for generalized multicategories by Cruttwell and Shulman (arXiv:0907.2460) proposes the normalized T-monoid. Another paper, by ...

### 3 Fong's Causal Theories: Is he also describing a Monad structure? Is the causal category also a bimonad?

Fong's paper Causal Theories: A Categorical Perspective on Bayesian Networks talks about causal theories. He describes words of random variables at the top of page 42: For the objects of CG we ...

### 5 Why are simplicial objects monadic over split (contractible) simplicial objects?

Given an augmented simplicial object $d_\bullet:X_\bullet \to \Delta X_{-1}$, suppose there's a simplicial map $s_\bullet :\Delta X_{-1}\to X_\bullet$ making $d_\bullet$ a deformation retract, i.e ...

### 3 A List-Like Frobenius Monad

Has anyone ever seen a Monad that is very much like the List Monad but is also a co-monad, and also a Frobenius monad? In this paper they give examples of List-like monads called Containers and they ...

### 2 Monad induced by actegory

It seems to be folklore that if we have an actegory, i.e. a monoidal functor from a monoidal category $C$ to an endofunctor category $Cat(D,D)$, we can obtain from it a monad on $D$. This appears for ...

### 8 Monads on Set with trivial algebras

In an earlier post, What is known about the category of monads on Set? the following observation was made: What's more, all but two monads on Set have the property that there exists an algebra ...

### 3 Is there any nontrivial monad on the category of graphs?

The question is in the title, but let me specify what I mean by the category of graphs. In the context of this question, the category of graphs is the category of symmetric irreflexive relations. ...

### 2 Lawvere theory and the Maybe monad

The Maybe monad is based on the endofunctor $- + 1$ (coproduct with the singleton set). Its Lawvere theory $L$ is supposed to be generated by one nullary operation (...

### 6 Has anybody studied strict/pseudo morphisms of monads?

There is a notion of morphism from a monad $T:\mathscr C\to \mathscr C$ to another one $T':\mathscr C'\to \mathscr C'$. It arose here on MO e. g. in "Functors between monads": what are these ...

### 10 Categories which are both monadic and comonadic over another category

I heard a professor say that $\lambda$-rings are both monadic and comonadic over commutative rings. Remark 2.11(a) on the nlab page says the same. What does it mean, intuitively, that a category is ...

### 4 Monads which are monoidal and opmonoidal

Do monads which are monoidal and opmonoidal have a name? (Bimonoidal?) In case they have already been studied, who can point me to a reference? More in detail. Let $(C,\otimes)$ be a symmetric (or ...

### 13 The reflexive free-category comonad-resolution is a cofibrant replacement of the discrete simplicial category associated with an ordinary category in the Bergner model structure on the category of small simplicial categories?

Let $X$ be the category of reflexive quivers, and let $Cat$ be the category of small categories. There exists an evident forgetful functor $U:Cat\to X$ sending a category $A$ to its underlying ...

### 6 is shuffle a Monad?

In the list monad, your map $TT \rightarrow T$ takes a list of lists and concatenates them to form a list. There is another way to take a list of lists and create a list, which is to shuffle randomly ...