Questions tagged [coalgebras]
For questions about coalgebras, comultiplication, cocommutativity, counity, comodules, bicomodules, coactions, corepresentations, cotensor product, subcoalgebras, coideals, coradical, cosemisimplicity, ...
9 questions from the last 365 days
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Coradical filtration for comodules is exhaustive
It is a standard fact in the theory of coalgebras and comodules that, given a coalgebra $C$ and a comodule $M$ over $C$, the coradical filtration
$$M_n := \Delta^{-1}(M\otimes C_0 + M_{n-1}\otimes C)$$...
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What is known about vector subspaces of polynomial rings closed under factors?
Let $R$ be a commutative ring. Call a nonempty subset $F$ of $R$ a factroid if it is closed under sums and factors. That is:
If $a,b \in F$, then $a+b \in F$, and
If $a,b \in R$ with $a\in R$ ...
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$C^\infty$-coring
We know that there the so called smooth algebras also known as $C^\infty$-rings. They can play an important role in modern treatment of differential geometry. Is there a coring analogue?
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Hopf algebras actions
Can you write down a general type of Hopf algebra action? How do you justify the name "action", when it is already used for group actions?
There must be a common core, if the same term is ...
user525442
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Reference for cocommutative coalgebras
I'm looking for references on cocommutative coalgebras where I can see them as kind of infinitesimal spaces. I'm trying to understand this post Why do Lie algebras pop up, from a categorical point of ...
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Is there a way in which "space" of random variables on $\mathbb{R}$ is canonically a coaugmented coalgebra?
Consider the "space" of random variables with finite expectation on $\mathbb{R}$ in the following sense: we fix the Borel $\sigma$-algebra on $\mathbb{R}$, and put random variables in ...
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Can't parse a statement in an article on coalgebras and umbral calculus
This question is cross-posted from MSE.
I am reading Nigel Ray's "Universal Constructions in Umbral Calculus" (1998, published in "Mathematical Essays in Honor of Gian-Carlo Rota", ...
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When are topoi of coalgebras atomic?
A geometric morphism is atomic if its inverse image is logical. Now consider a Grothendieck topos $\varepsilon$ and its terminal geometric morphism $\Gamma : \varepsilon \rightarrow Set$, topos is ...
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Has anyone studied factoring as a CO-product?
In factorization, like integer factorization, you start with an integer and end up with a kind-of list of pairs of other elements, namely the factors.
I want to explore the "Co-ness" of this....
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