2,085 reputation
522
bio website N/A
location Glasgow, Scotland
age 25
visits member for 2 years, 8 months
seen 5 hours ago

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


Jan
4
accepted Is $(gf)(X) = g ( f(X))$ in a category?
Dec
24
comment Exactness of Colimits
unless $\bigoplus $ is sometimes used as a symbol for colimit?
Dec
24
comment Tensor product and exterior algebra
For your first question define a bilinear map on M x N and use the universal property of the tensor product. This will give you a linear map on the tensor product. You can similarly define a bilinear map on N x M which will give a linear map on the tensor product. You can check they are inverses. To define maps on tensor products, as a matter of course you should define bilinear maps on M x N and then use the UP
Dec
24
comment Exactness of Colimits
@Mariano perhaps this should have been emphasised in the source. However in the source it is asserted that the other two colimits are just in fact coproducts. Is it true that we get the coproduct when we take the colimit of $ X_\bullet $and $ X / X_\bullet $ if $ I $ is directed/filtered?
Dec
24
asked Exactness of Colimits
Dec
20
comment Is $(gf)(X) = g ( f(X))$ in a category?
@ZhenLin Could you explain why having pullbacks means that the images compose? I am having trouble seeing it. Thanks a lot
Dec
20
comment Is $(gf)(X) = g ( f(X))$ in a category?
@Berci actually that is the terminology that Mitchell uses
Dec
20
comment Is $(gf)(X) = g ( f(X))$ in a category?
@Berci I misspoke. I meant to say that the category has epi-mono factorisations
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?