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2d
comment Equivalence between category of $R$-modules and $S$-modules
what is $M_n(A)$?
Apr
30
comment Three theorems for the price of one? (like duality)
This is a very good question. Please be patient for a few days and I wll write an hopefully good answer.
Apr
27
comment integral domains and field of fractions
Yes, this adjunction is a reflection and $\mathcal F$ is the reflector
Apr
24
comment The colimit of all finite-dimensional vector spaces
@MartinBrandenburg now it's 7 upvotes
Apr
22
comment No natural transformation
That's better !
Apr
21
comment No natural transformation
Dear iwriteonbananas, don't you think that you should at least put a reference to the textbook you are so shamelessly copying from?
Apr
18
comment Categorical Banach space theory
Martin and @tcamps Thank you for the references
Apr
17
comment Categorical Banach space theory
Well, the functional analysis arguments which make Banach spaces preferable over NormedVectorSpaces can't be described categorically? If yes, then these are (some of) the special properties that differentiate the 2 categories. Perhaps you could exemplify some of these arguments and we can see if there is a way to express them categorically.
Apr
17
comment Categorical Banach space theory
Could you please give an introductory reference to " categorical Banach space theory"?
Apr
15
comment Isomorphic categories
I see, thank you
Apr
13
comment Isomorphic categories
$K [X] $ is the ring of polynomials? If so, could you please explain how you associate $(V,T) $ to a module over the polynomials?
Apr
10
comment Is Stokes' Theorem natural in the sense of category theory?
Very nice question!
Apr
10
comment Name of some category with two objects
@MartinBrandenburg what is MP?
Apr
6
comment Examples of categories which appear naturally without objects
Yes, and i was thinking at groups, but the OP has already discounted this. I do not think thereis anything better than "monoids with a partial composition" After all this what categories really are.
Mar
30
comment Inverse limit of isomorphic objects
@ThomasAndrews what do you mean by $G_n $?
Mar
24
comment Universal Properties and Isomorphisms
The quoted definition seems to be more general than the one given by Maclane (and others). Maclane defines a universal property when you have a terminal object in a SLICE category of the original category where the object was living. The def. Given by Aluffi seems to me a bit weak. Check wikipedia for similar defs.
Mar
22
comment Two categories sharing the same objects and morphisms
When two such categories $\mathcal{C}$, $\mathcal{C}'$ exist, what are they? Equivalent? Isomorphic?
Mar
20
comment Why the whole exterior algebra?
@MarioCarneiro what matrices are you referring to? I never said anything about matrices. We are talking about (graded) vector spaces or modules and why they are useful in mathematics
Mar
10
comment Cartesian Product characterization in Rel Category (Category of sets and relations) in simpler terms
....This description is made using concepts from monoidal categories,so I think that you need to study them a bit if you want to understand this part of the answer given by Zhen Lin.
Mar
10
comment Cartesian Product characterization in Rel Category (Category of sets and relations) in simpler terms
Qartal the Q&A you mentioned has 2 parts.The first part proves that the categorical product of 2 objects $Y$, $Z$ (which are sets) in the category $Rel$ is given by the object (which is a set) that you would call "the disjoint union of $Y$ and $Z$".This part has nothing to do with the cartesian product of $Y$ and $Z$.The second part describes/characterizes the object of $Rel$ that you would call "the cartesian product of $X$ and $Y$"...