Can someone explain the definition of epimorphism to me?

No, I am studying out of a book and don't know anyone in real life to ask. You are treating this like a "homework" thread when it clearly isn't one. Banned or not doesn't change the fact you're an asshole.

Where's the confusion?

That example makes sense, but before thread is banned (this clearly isn't homework) can you answer

announcing your reports is against the rules and this clearly isn't a homework thread
sorry, brainlet

Okay, that'll be an even longer ban now. Learn to control your emotions and think. You'll need that skill later in life when the consequences will be more than getting banned. People aren't going to respect you.

Not sure what you're talking about. "onto" and "surjective" are synonymous. It requires exactly what's specified. Namely, that two functions coinciding on the codomain of f implies they are the same on their domain.

There's many examples that can easily be found online. Fairly trivial examples include surjective maps in Set and Grp.

Less trivial examples include the continuous maps between topological spaces in the category of Hausdorff spaces.

I am new to category theory, Hom(Z,A) means all the arrows from Z to A right? But does it guarantee that there is an arrow from Z to A?

My confusion is still with

if every element in X isn't mapped then f is not a function you fucking faggot
get your definitions straight before posting this garbage

I think of epimorphisms as being morphisms whose image "determines" morphisms coming out of the codomain. (This is an intuition rather than a definition, since epimorphims make sense in categories where images don't make sense.)

Less trivial examples than surjective functions include continuous maps with dense image (in topological spaces) and the inclusion of an integral domain into its field of fractions for example Z -> Q (in unital rings). In both these cases, the image of the epimorphism "determines" outgoing morphisms in the sense that two continuous maps which agree on a dense set must be the same, and two ring homomorphims which agree on Z must be the same.

Dude chill, he's trolling.

>This mad

wew lol

Hom(Z,A) just means all of the morphisms from Z to A
There is only a morphism between any Z and A if it's allowed by the morphism definition in the category in question

Basically in set theory

f: X->Y to be onto requires every element in Y to have something mapped to it. It dosn't require element element x map to an element y, only that every element y has a mapping from X to it.

Does the same apply for the definition in category theory? i.e., does it require an arrow from every object in X or does it only require that every object in Y has an arrow?

yeah i get mad when faggots don't bother to learn basic faggot definitions before calling other people wrong

t mathfag

it's a partial function, you're talking about total functions. but i guess i can talk about total functions here.

That's understandable, I wish I could quell your anger because it's very stressful to endure

A monad is a monoid in the category of endofunctors

the definition of a FUNCTION requires every element of the domain to have an image in the co-domain
a """partial function""" is nothing more than a relation on two sets you incredible faggot

t. mathfag

ty

can you give me a simple set theory example that satisfies the definition of epimorphism? i think i'd get it if i could see an example.

Is this one of an epimorphism?

f(x)=1
f(y)=2

g1(1)=a
g2(1)=a

g1(2)=b
g2(2)=b

"In" doesn't make sense in category theory. Objects in category theory are axiomatically defined things which only serve as the domain and codomain of morphisms, and being able to talk about elements is not part of those axioms. In many of the important examples, especially the most accessible ones, the objects are things like spaces or groups which are "basically" sets and so you can talk about elements in those cases, but elements aren't part of the language of category theory and there are lots of important examples like the category of sheaves over a space where it doesn't make any sense to talk about elements.

sure
let [math]A = \mathbb{Z}[/math] and [math]B = mathbb{N}[/math] and define a function [math]f[/math] such that
[math](\forall z \in \mathbb{Z})(f(z) := |z|)[/math]
Here we'll assume that [math]N \subseteq \mathbb{Z}[/math] for simplicity.

Now all you have to do is prove this satisfies the definition of a monomorphism.

t. mathfag

who is your epi? f?
you can't say whether f is an epimorphism without providing is domain and co-domain
also it's meaningless to mention g since f must satisfy the epimorphic property for ALL other morphisms in your category

[math]\mathbb{N}[/math]*

basically as this guy said; you can use ZF Set Theory as an example of a category, but Category Theory is largely incompatible with Set Theory and it's meaningless to talk about relations like [math]\in[/math] in many relevant categories

Domain {1,2}
Codomain {a,b}

I was trying to show that this function is an epi. I thought I was trying to g1/g2 is an epi? But would it make more sense to say f is an epi?

I was trying to say g1 * f = g1 * f => g1 = g2

This question doesn't make sense and it sounds like you need to review the basic definitions. Read this book: arxiv.org/pdf/1612.09375.pdf

g1 * f = g2 * f => g1 = g2 (correction)

ok i'll look at the book i was trying to read wikipedia articles, didnt have a structured approach

the problem is you're using specific g's
you need to prove that
[math]g_1 \dot f = g_2 \dot f \implies g_1 = g_2[/math] for all morphisms [math]g: X \to Y[/math]

I thought you said you were following a book.
If your book is shit (which it seems like it is, unless it's just you that's retarded) you should download a copy of Chapter 0 by Aluffi
The first chapter on category theory is great for self-study and should answer all your questions

t. mathfag

for all morhpisms [math] g_1: X \to Y[/math] and [math]g_2: X \to Y[/math]*

>Understanding equations

in school I always thought like a=1 and b=2 and c=3 and so on and so forth....

... what the fuck are you on about faggot

t. mathfuck

well i am sorta using a shit book too. i'll look at what you're talking about. what math background do i need to read it? I'm basically like a freshman, but know basic math proofs/discrete math

if you know how to construct and read a proof just dive right in and you should be fine

t. mathfreak

Aluffi is really accessible so you pretty much just need to know basic logic/proof stuff, which it sounds like you do.

OK I'm diving in right now. You'll probably see future threads by me. I'm not btw

Thanks guy.

Also, any good youtube videos to follow for lectures?

np my dude
i only use youtube for starcraft, speedruns, and politics so i can't help you there

best of luck

t. mathnigger

youtube.com/user/TheCatsters

These are more relevant to the book in

great, alright im bouncing off here to read. thanks again