Questions tagged [universal-property]

For questions about universal properties of various mathematical constructions.

In various branches of mathematics, a useful construction is often viewed as the “most efficient solution” to a certain problem. Reference: Wikipedia.

The definition of a universal property uses the language of category theory to make this notion precise and to study it abstractly.

521 questions

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3 answers

I am trying to write a disproof for a universal statement

I have a statement that says, for all $x$ in the set of integers, there is some $y$ in the set of naturals, such that $y$ is less than $x$. I know that this is false because $x$ can be negative, and a positive is not less than a negative. I'm…

universal-property

asked Dec 11 '17 at 13:27

Allie Grace

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2 answers

How is this an example of a Universal Property?

I'm totally lost on this problem, which is from a set of notes by Tom Leinster on Category Theory: Let $\phi: G \to H$ be a homomorphism of groups. Associated with $\phi$ are the diagrams $ker(\phi) \xrightarrow{i} G \xrightarrow{\phi} H$ and…

universal-property