How do you write the -- in Hom(--,B) ?

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In summary, the double dash (--) in "Hom(--,B)" is a placeholder used to indicate two mathematical objects or spaces being compared in the context of homology. Its purpose is to allow for more general statements about homology without specifying the specific objects being compared. It is necessary in order for the statement to make sense and should not be replaced with other symbols.
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quasar987
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I want to know how to write the dash in Hom(--,B)
Hello!

Here's a piece of a print screen I did on Wikipedia's page on "Hom functor":

1660438697202.png


Does anybody knows how to do that dash that's longer than a mere minus sign?
 
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  • #2
What is wrong with \operatorname{Hom}(-,X) ?
##\operatorname{Hom}(-,X)##
 
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  • #3
fresh_42 said:
What is wrong with \operatorname{Hom}(-,X) ?
##\operatorname{Hom}(-,X)##
Not a thing! I was certain that I had tried that in Overleaf and it didn't look good. But now I tried it and it looks fine.
 

1. How do you write the -- in Hom(--,B)?

To write the "--" in Hom(--,B), you would use the notation Hom(--,B), where the first blank represents the domain of the homomorphism and the second blank represents the codomain.

2. What is the significance of the "--" in Hom(--,B)?

The "--" in Hom(--,B) represents a placeholder for the domain and codomain of the homomorphism being discussed. It allows for a more general discussion without specifying specific objects.

3. Can the "--" in Hom(--,B) be replaced with specific objects?

Yes, the "--" can be replaced with specific objects to represent a specific homomorphism. For example, Hom(G,H) would represent the set of all homomorphisms from group G to group H.

4. What is the purpose of using Hom(--,B) in mathematical notation?

The notation Hom(--,B) is used to represent the set of all homomorphisms from an unspecified object to a specific object B. It allows for a concise representation of a set without needing to specify specific objects.

5. Are there any other notations that can be used to represent homomorphisms?

Yes, other notations for homomorphisms include Hom(A,B) or Hom(A,B) for specific objects A and B, and Hom(G,H) for specific groups G and H. These notations can be used interchangeably with Hom(--,B) depending on the context of the discussion.

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