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Nov
7
answered Connection between categorical notion of adjunction and dual space/adjoint in vector spaces
Nov
5
comment Identifyng objects in a category
I never said the question was "stupid" or anything (I even upvoted it).I never said the question did not make sense at all. My advise was of a more general nature - a tactics you might say: whenever you want to invent/reinvent/discover/rediscover something in category theory, think at morphisms first, then objects will fall in line automatically. Granted,we intuitively all think in terms of objects, but the challenge (and the reward) in category theory is to think in terms of morphisms. Is this not true?
Oct
31
comment Functor between two categories
thank you.This result does not seem to be readily available everywhere, otherwise you would not need to ask us here. Is your course/homework online, so that I can see it ?
Oct
31
comment Functor between two categories
Was this question inspired by some book/text? Could you please post a reference?
Oct
30
reviewed Approve Solving a differential equation 1st order
Oct
30
revised Derive the unit from the adjunction
edited some text
Oct
30
comment Derive the unit from the adjunction
CWM 2nd ed. page 80 gives a clear derivation of the naturality of $\theta$ (he calls it $\phi$) both in $C$ and in $D$. This is a more general result than the one you wish to obtain. I also edited a couple of things.
Oct
29
comment Example of a homomorphism with a right or left inverse function that its right or left inverse is not a homomorphism
Please note that left and right inverses are not unique in general. So you should not ask about the left/right inverse, but about a left/right inverse.
Oct
27
revised Is a subobject classifier logically equivalent to set-inclusion?
added last paragraph
Oct
27
awarded  Electorate
Oct
27
answered Is a subobject classifier logically equivalent to set-inclusion?
Oct
26
revised Definition of a coproduct and its universal property - connection?
Edited grammar, syntax and formulas
Oct
26
revised Group objects in category of $\mathcal{Set}$ are groups - How to prove it?
Edited grammar in title
Oct
20
comment Relationships between initial/terminal objects and initial/terminal morphisms (if any) in the same category.
Alex it is a good answer in search of a question :-) in general limits, universals, adjoints and kan extensions can all be expressed in term of each other. This is explained eg. In CWM
Oct
20
comment bijective homomorphisms between non isomorphic posets, example , explanation needed
Awodey gives similar (or same ) exammple somewhere else when he speaks of invariants. Read further
Oct
16
answered A connected groupoid is equivalent to a groupoid with one object
Oct
16
comment Natural isomorphisms of the forgetful functor
Thank you @Pece I have seen the corresponding edit
Oct
15
comment Natural isomorphisms of the forgetful functor
sorry if this is a silly question, but I am a bit groggy right now, but what is g and what is g^z? are you describing the components of natural transformation $\eta (z)$ ?
Oct
15
comment Natural isomorphisms of the forgetful functor
Nice question! Does it come from a textbook? if yes, which one?
Oct
10
comment How to prove uniqueness of *wannabe* final object in a slice category?
Aluffi himself in his book hints at how you can attack this problem, by checking the various projections, as also @martin suggests. However I understand and share your appetite for a categorical proof. If you are a bit patient, I will write one shortly