Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

i've constructed a couple of equalizers in the category of sets/graphs. If anyone could tell me if my equalizers turned out right, that would be very much appreciated.

example of an equalizer in the category of sets

O1 = {a1, a2, a3, a4} --set 1
O2 = {b1, b2, b3, b4} --set 2
f12 = {(a1->b1), (a2->b2), (a3->b3), (a4->b4)} --set morphism 1
g12 = {(a1->b1), (a2->b1), (a3->b2), (a4->b4)} --set morphism 2

solution (correct?)
eq_kernel = {a1, a4}
eq_injection = {(a1->a1), (a4->a4)}

example of an equalizer in the category of graphs

graph object 1
GO1 = (E1,V1,SRC1,TGT1) -- graph object
E1 = {e11, e12} -- edges
V1 = {v11, v12} -- vertices
SRC1 = {(e12->v12), (e11->v11)} -- source
TGT1 = {(e12->v12), (e11->v11)} -- target

graph object 2
GO2 = (E2,V2,SRC2,TGT2) -- graph object
E2 = {e21, e22} -- edges
V2 = {v21, v22} -- vertices
SRC2 = {(e22->v22), (e21->v21)} -- source
TGT2 = {(e22->v22), (e21->v21)} -- target

gmorph1 = (Dom1, EdgeArrow1, NodeArrow1, Codom1)
Dom1 = GO1
EdgeArrow1 = {(e12->e22), (e11->e21)}
NodeArrow1 = {(v12->v22), (v11->v21)}
Codom1 = GO2

gmorph2 = (Dom2, EdgeArrow2, NodeArrow2, Codom2)
Dom2 = GO1
EdgeArrow2 = {(e12->e21), (e11->e21)}
NodeArrow2 = {(v12->v21), (v11->v21)}
Codom2 = GO2

solution (correct?)

EEQ = {e11} -- edges
VEQ = {v11} -- vertices
SRCEQ = {(e11->v11)} -- source
TGTEQ = {(e11->v11)} -- target

EQ_INJECTION = (DomEQ, EdgeArrowEQ, NodeArrowEQ, CodomEQ)
EdgeArrowEQ = {(e11->e11)}
NodeArrowEQ = {(v11->v11)}


share|cite|improve this question

So both your examples are correct. The way you wrote all that is really dense and more complicated than need be though.

share|cite|improve this answer
Thanks a lot, David! How would I go about writing it less complicated? – spirit Mar 29 '11 at 19:26
Using latex and a more standard mathematical presentation style. In particular, don't be afraid to write sentences. – BBischof Jul 23 '11 at 14:09

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.