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Sep
10
comment Identity in a category
Omar's demonstration is typical in these kind of proofs: identities (or units or neutral elements) are uniquely determined by their defining equations, if they are already known to exist
Sep
6
comment Where can I learn more about order-reflecting functions? And is the following result well-known?
Nice remark that the proof doesn't use the properties of ≤. I am a bit confused by your definition though. Perhaps there are some typos. The op-functor is $F$ or is $F^{-1}$ ? Also, the op-functor should go in the opposite direction to $F$, correct? "op" stands for (or reminds to) "opposite"?
Sep
1
answered What can we conclude about the natural projection maps?
Aug
31
comment Direct products in a partially ordered category
I am not sure I understand your question, but if you are trying to characterize a product in a poset category, then you should reverse the arrows of $\pi_0$ and $\pi_1$ and $\phi$ should be the largest lower bound to the family of objects
Aug
25
revised Understanding adjoint functors
Edited isomorphism formula
Aug
25
suggested approved edit on Understanding adjoint functors
Aug
17
revised Complete abelian categories with projectieve generators are fully abelian.
edited small typos
Aug
17
comment Complete abelian categories with projectieve generators are fully abelian.
Welcome to Math.SE :-) I suggest you choose a nickname (your real name or a fantasy name), so that other users may more easily recognize you later.
Aug
17
suggested approved edit on Complete abelian categories with projectieve generators are fully abelian.
Aug
9
revised Functionally structured spaces and manifolds
edited small typos
Aug
9
suggested approved edit on Functionally structured spaces and manifolds
Aug
6
comment Concrete balanced category
Would the downvoter mind to explain his/her downvote? The OP wrote: if every bimorphism is an iso we have a balanced category, if we have a balanced category , is it true that every bimorphism is an iso? I simply said : yes it is true. What's wrong with it?
Aug
6
answered Concrete balanced category
Jul
29
comment Identity of Initial Elements in a Category
...Isomorphism is a derived concept in category theory and its definition depends on equality (the composition of a morphism with its inverse is EQUAL to the identity morphism)
Jul
29
comment Identity of Initial Elements in a Category
the comment by @Kris , taken at face value, is meaningless. Established mathematical theories (like Category theory) are always logically consistent. otherwise they are discarded right away (just like Frege's naive set theory). Category theory is based on logic with equality and equality is used extensively for ex. to test whether a morphism is monic or epic. The point of category theory, as explained also by Qiaochu Yuan, is that the properties that we should care about should be invariant for isomorphic objects....
Jul
26
revised Proof in Hungerford about natural isomorphisms of multifunctors
edited formula
Jul
26
suggested approved edit on Proof in Hungerford about natural isomorphisms of multifunctors
Jul
26
comment Proof in Hungerford about natural isomorphisms of multifunctors
It does hold for multifuntors too. The author just wants you to write down the (more general) equations in this case. I would replace "equivalence" with "isomorphism" in your text and perhaps use the more common id in place of $\varepsilon$ .
Jul
24
comment An example of a monomorphism that is not an equalizer in “Abstract and Concrete Categories — The Joy of Cats”
did they answer to your mail?
Jul
9
revised Clarification of the Definiton of Locally Small Categories
Added last paragraph