Past exam of the mathematics course of the University of Cambridge / 2009 / iii / Paper 23 / 4 / b

Table of contents
- Solution b

Solution

p i = 1_{A}

give

(i p) i = i

, so

i

equalizes

i p

and

1_{B}

. If

h : X \to B

satisfies

(i p) h = h

, put

k = p h : X \to A

. Then

ik = i p h = h

. If

k^{'}

is another such factorization, applying

p

gives

k^{'} = p i k^{'} = p h = k

. This proves

i : A \to B is the equaliser of i p and 1_{B} .

In particular the inclusion in a retract in a category is a monomorphism.

 Ancestors (10)

 View article source

 Discussion (0) New discussion

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version