2,038 reputation
420
bio website N/A
location Glasgow, Scotland
age 25
visits member for 2 years, 2 months
seen Mar 17 at 12:24

I am just a student trying my best to cram maths into my head.


Dec
19
comment Is $(gf)(X) = g ( f(X))$ in a category?
I don't think it is true in general, but it is true for categories which are balanced and have epimorphic images [Mitchell, Theory of Categories]
Dec
19
revised Is $(gf)(X) = g ( f(X))$ in a category?
edited title; edited title
Dec
19
asked Is $(gf)(X) = g ( f(X))$ in a category?
Dec
17
comment Smallest subobject in an abelian category containing a set of objects
I have just realised that is true, because we are talking about subobjects and hence any factorisation must be a mono (and unique).
Dec
17
comment Smallest subobject in an abelian category containing a set of objects
I misunderstood "contains $A_i$" to mean "have $A_i$ as a subobject." Thanks for clarifying. Is it necessarily true that $A_i$ will be a subobject of some $Y$ if it factors through $Y$ ?
Dec
17
accepted Smallest subobject in an abelian category containing a set of objects
Dec
17
asked Smallest subobject in an abelian category containing a set of objects
Dec
14
comment Set of generators in an abelian category - two definitions
Would it be to correct to say that in a category where every mono is regular, that every epi is extremal? I think so, because if we factor $f$ as $f = f' m$ for some mono m, and suppose that $st = tm$, we get $smf' = sf = tf = tmf'$ which implies that $t = s$ which tells us $m$ is an epi. Since it is a regular mono too it is an iso
Dec
13
accepted Set of generators in an abelian category - two definitions
Dec
13
asked Set of generators in an abelian category - two definitions
Dec
11
awarded  Tumbleweed
Dec
4
accepted Why can I choose to work in a strict monoidal category without loss of generality?
Dec
4
comment What would be an interesting example of a Co-algebra with a base category other than Set?
You can also learn about corings which are coalgebras in the category of $(A,A)$-bimodules where $A$ is some unital associative algebra over a commutative ring $k$.
Nov
19
accepted Existence of a Coend in a Monoidal Category
Nov
16
asked Why can I choose to work in a strict monoidal category without loss of generality?
Nov
5
asked Is the boundary map induced by a good pair $(D^2, S^1)$ equal to multiplication by $2$?
Oct
29
comment Does tensoring flat modules preserve minimal generating sets?
Perfect, thank you.
Oct
29
accepted Does tensoring flat modules preserve minimal generating sets?
Oct
26
comment Does tensoring flat modules preserve minimal generating sets?
@navigetor23 I tried to show this, but I couldn't get it to work... If $k$ is local then we have an ideal of non-units $I$ . If we define $f \colon k \to M$ by $f(\alpha) = \alpha m_i$ this map will only descend to a quotient map $\tilde f \colon k/ I \to M $ if $f(I) = 0$... but is it true that $\alpha$ is a non-unit implies that $\alpha m_i = 0$? The converse of that statement is true however by hypothesis.
Oct
26
revised Does tensoring flat modules preserve minimal generating sets?
added 306 characters in body