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Results tagged with polynomials
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user 2811
Questions in which polynomials (single or several variables) play a key role. It is typically important that this tag is combined with other tags; polynomials appear in very different contexts. Please, use at least one of the top-level tags, such as nt.number-theory, co.combinatorics, ac.commutative-algebra, in addition to it. Also, note the more specific tags for some special types of polynomials, e.g., orthogonal-polynomials, symmetric-polynomials.
10
votes
1
answer
526
views
Is the evaluation of polynomial functors appropriately continuous?
I'd like a nice proof of the following fact.
Let $C$ and $D$ be categories, and let $\mathbf{Cat}/(C\times D)$ be the usual (1-categorical) slice category whose objects are triples $(X,F\colon X\to C …
- 8,659
4
votes
0
answers
125
views
Can a non-free monad have non-trivial "quine"?
Let $\mathbf{Poly}$ denote the category of polynomial functors on $\mathbf{Set}$, and let $\mathfrak{m}\colon\mathbf{Poly}\to\mathbf{Poly}$ be the free monad monad, i.e. the functor that sends every p …
- 8,659
3
votes
Is the evaluation of polynomial functors appropriately continuous?
Ok, this follows trivially from the construction of limits in ${\bf Cat}$.
Let $I\ $ be a small category, let $X\colon I\to{\bf Cat}\ $ denote a functor, and let $Y=\text{colim}_{i\in I}X_i\ $ be it …
- 8,659