Recent content by galoiauss

Here's another example I just ran into: If * represents a single point, then colim(X<--*-->Y)=XvY, where v represents the wedge product. Where is XvY supposed to fit into the diagram X<--*-->Y? Is it just placed in there and we make arrows from every vertex pointing to it? How do we know...

I see, that makes sense. Thank you. So in general, if we're given a diagram (such as the examples above) how are we supposed to find the colim? For example, how did you determine that Y is colim for the first example? I want to try to work out the 2nd one myself and check with you if you don't mind.

I'm sorry, I'm confused because the example said there were 2 maps in X==>Y, not 1.

On a very informal level. I haven't learned category theory, but one of my teachers introduced some basic terminology and ideas. He mentioned something about if there's a commutative diagram, with a lot of things D going into the colimit, and for any other object Z that the D's map to, there is...

No, the original colim notation is accurate. I would appreciate knowing what the relationship is. Thank you.

the only thing I'm familiar with for colimits is if I have a diagram, the colimit in the diagram is the object through which everything factors. I'm not familiar with what a cofibration is; is there a more elementary way of interpreting the above examples?

Can someone please explain to me what the following notation/objects are: (Here X,Y are topological spaces) colim(X-->Y<--X) where the first arrow is a map f, the second is a map g. colim(X==>Y), where there are 2 maps f,g from X to Y (indicated by double lines, but couldn't draw 2 arrow...

Just wondering, what is the general consensus on whether physics or math is a more respectable and "harder" intellectual field. I'm a mathematician, and I know both can be very hard, but just wanted to know on a simple level. I'm asking this in the same light as how people usually rank the...