I am reading a paper where the author uses colons in the description of groups. Example (not verbatim): "This subgroup is isomorphic to (Z_5 X A_4):Z_2". Several subgroups are described in the same way (as (G_1 x G_2):G_3) throughout the paper.
I have seen the colon in G:H to indicate the...
Thank you! I have some background in linear algebra and group theory, but I am just starting categories. I am trying to do some independent study in Categories for the Working Mathematician, and sometimes just a little clarification or explication helps so much when working on the exercises.
Thanks! (You are right, of course, I was being sloppy in using the term "uncountable" as I did.)
So suppose you had a function in SET, something like R^2 -> R^2 given by (x_1,x_2) -> (x_1,0). Would this arrow actually go from R^2 to itself, or to some distinct set object indicating the...
Can someone give a quick description of the objects in the category SET? In particular, are sets distinguished by anything more than cardinality (i.e. R^2 has the same cardinality as R--are they distinct objects in SET, or is there just one "uncountable set" object?)
Answers/help much...