Need to find a functor T : Set &#x2192;<!-- → --> Set such that Alg(T) is concretely

Wisniewool 2022-07-09 Answered
Need to find a functor T : Set Set such that Alg(T) is concretely isomorphic to the category of commutative binary algebras.
The first idea is that the functor is likely to map object X O b ( to the X × X because then we have to get a binary algebra, i.e., the operation X × X X, which have to be commutative.
So the question (if these thoughts are right) is: how to map X to X × X to get later a commutative binary algebra?
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

talhekh
Answered 2022-07-10 Author has 15 answers
Hint: Giving a function f : A / ε B from a quotient set A / ε is the same as giving a function f ¯ : A B that satisfies a ε a 1     f ( a ) = f ( a 1 ).
Apply this for A = X × X and a suitable equivalence relation ε on it.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-04-25
How do I factorize x61 over GF(3)? I know that the result is (x+1)3(x+2)3, but I'm unable to compute it myself.
asked 2022-07-02
By conjugate linear transformation, I mean under scalar multiplication instead of C ( a f ) = a C ( f ), I would have C ( a f ) = a ¯ C ( f ), where a is a constant complex number, and C is the transformation.
asked 2021-10-02

Find 63×62

asked 2020-12-30

Since we will be using various bases and the coordinate systems they define, let's review how we translate between coordinate systems. a. Suppose that we have a basisB={v1,v2,,vm}forRm. Explain what we mean by the representation {x}g of a vector x in the coordinate system defined by B. b. If we are given the representation {x}B, how can we recover the vector x? c. If we are given the vector x, how can we find {x}B? d. Suppose that BE is a basis for R^2. If xB=[12] find the vector x. e. If x=[24] find xB

asked 2022-06-02
I have a system of non-linear equations of the form
A x 1 B exp ( C x 1 ) = k 1
A x 2 B exp ( C x 2 ) = k 2
A x 3 B exp ( C x 3 ) = k 3
where [ x 1 , x 2 , x 3 ] and [ k 1 , k 2 , k 3 ] are known. The couple of constants [ A , B , C ] is the unknown. The solution of this non-linear system of equations is given here: Solving a system of non linear equations
We must now ensure that B < 0 at all times. How would you find one couple [ A , B , C ] that best approach the solution of the system, with B < 0.
asked 2021-12-12
Find, correct to the nearest degree, the three angles of the triangle with the given vertices.
A(1,0,1), B(3,4,0), C(1,3,5)
asked 2021-08-10
Begin by graphing
f(x)=log2x
Then use transformations of this graph to graph the given function. What is the graphs

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question