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# Questions tagged [monads]

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129 questions
118 views

### Relative cocompletion of a category

$\newcommand{\k}{\mathbf k}$ $\newcommand{\A}{\mathcal A}$ $\newcommand{\B}{\mathcal B}$ $\newcommand{\C}{\mathcal C}$ I'm wondering if anyone knows a reference for the following construction: let $\k$...
84 views

### U-split coequalizer preserved by coproduct

Let $C$ be a nice symmetric monoidal category and let $T$ be a monad on $C$ such that we have a monadic adjunction $$F:C\leftrightarrow T\text{-}alg(C):U$$ Suppose that $a\rightrightarrows b$ is a ...
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### Monad, algebras and reflexive coequalizer

Suppose we have an adjunction of categories $F:M\leftrightarrows N:U$. We define the associated (co)monad $G=F\circ U$. For any object $x\in N$ we define the simplicial resolution of $x$ given by  ...
150 views

### What category of toposes is monadic over the 2-category of groupoids?

Excuse my lack of understanding of monadicity, but I have been looking at toposes and monads. I see Lambek showed that the category of Toposes are monadic over the category of categories. I see the ...
48 views

### Schemes for conditional distributions (monads)

(Note: This is a heuristic question. I'm trying to work out if this idea makes sense. I don't have much background in this area, so apologies if I'm wide of the mark.) Suppose you have a monad ...
72 views

### Is there a natural transformation from Lists to Domains of Lists

The list monad, $(L, \mu_L, \eta_L)$, on $Set$, takes a set to its set of lists, with $\mu_L : L \cdot L \rightarrow L$ being concatenation of lists. Given a set of lists, there is a natural way to ...
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### The multi-set monad and modules

I am trying to analyze the category of algebras for the finite free commutative monoid monad, aka the finite multiset monad. This monad is frequently described as having a multiplication that takes a ...
267 views

A unidetermined contramonad is a 2-monad $T : {\cal C}\to \cal C$ such that $T$ is contravariant, i.e. a contravariant endofunctor; the multiplication $\mu_A : TTA \to TA$ is determined as $T\eta_A = ... 1answer 155 views ### Codensity monad is idempotent? Let$j: A \to B$be a fully faithful functor. When$j$has a left adjoint$L$, the codensity monad$\text{Ran}_jj$will coincide with the monad$jL$and thus will be idempotent, because$A\$ is ...

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