All Questions
Tagged with algebra ct.category-theory
9 questions
-1
votes
1
answer
151
views
What theorems are interesting in a monad?
In a monad, one can prove that the Kleisli composition is associative, and eta is its right and left unit, this is the famous monoid in the endofunctor category:
...
- 123
3
votes
1
answer
131
views
Can the initial algebra of a 2-variable polynomial functor be computed on the diagonal?
Given a polynomial functor $F$, its initial algebra is denoted by $\mu X.F(X)$.
Now, if $F$ is a 2-variable polynomial functor, $Y \mapsto \mu X.F(X,Y)$ turns out to be functorial and we can, again, (...
- 509
8
votes
2
answers
923
views
What category are Tagless Final Algebras final In?
The Haskell and Scala community have been very enamored recently with what they call tagless final 'pattern' of programming. These are referenced as dual to initial free algebras, so I was wondering ...
- 595
2
votes
1
answer
90
views
Does an initial algebra for a class have to belong to the class itself?
In the context of algebraic data types, a concept of initial algebras is usually defined, e.g., in the following way:
An algebra $S$ is initial in a class $C$ of algebras iff for every $A\in C$ ...
user49685
10
votes
2
answers
1k
views
What kind of theoretical object corresponds to a C++ concept?
I am lacking a background in theoretical computer science but I would have liked to understand to what kind of theoretical objects C++ concepts corresponds to. Basically, C++ concepts allow to define ...
- 307
33
votes
12
answers
7k
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Algebra oriented branch of theoretical computer science
I have a very strong base in algebra, namely
commutative algebra,
homological algebra,
field theory,
category theory,
and I am currently learning algebraic geometry.
I am a math major with an ...
- 481
2
votes
0
answers
76
views
Composition series and isogeny
I'm not sure this question is appropriate for this site, but it might have some connections with computational algebra.
Consider a fixed "category" $\sf{Cat}$ (in the sense of category theory, but ...
- 1,312
20
votes
4
answers
3k
views
Data Structure isomorphisms
Disclaimer: I am not a CS theorist.
Coming from abstract algebra, I'm used to dealing with things that are equal up to a isomorphism - but I'm having a trouble translating this concept to data ...
- 203
6
votes
2
answers
673
views
Proof of a unique homomorphism from an initial object
What is the proof that there is only one homomorphism from an initial object to another object?
- 293