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7
votes
Computability of infinite-dimensional vector space
Short answer
The general answer is that computability is easy for locally compact spaces, doable for separable spaces, and hard for non-separable spaces.
The short anwer for a particular example, na …
9
votes
Formal representation of an abstraction hierarchy
You are working on your PhD. Saying "I am not well versed in $X$" is not an excuse. And if you're good, then saying "my advisor does not know $X$" is not an excuse either.
You are using monoids where …
5
votes
What is necessary and/or sufficient requirement for a subring of a field to be computable?
$\Sigma$-algebra. … Because $\nabla$ preserves products, it maps $\mathcal{A}$ to a $\Sigma$-algebra $\nabla \mathcal{A}$ in $\mathsf{Asm}$. …
7
votes
Does an initial algebra for a class have to belong to the class itself?
Yes, the initial algebra is by definition one of the members of the class for which it is initial.
You may however be interested in the category-theoretic concept of a limit. … The limit is like an initial algebra. …