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Apr
24
comment Zorn's Lemma Application for Finding Maximal Submodule?
Since $\bar L$ is a maximal element in $\mathscr{F}$ you have that for every other element $L \in \mathscr{F}$, that is every other submodule of $M$ such that $x \not \in L$ and $N \subseteq L$ you have that if $L \supseteq \bar L$ then $L = \bar L$. This is the definition of maximal element of a poset.
Apr
24
comment Zorn's Lemma Application for Finding Maximal Submodule?
Because you're element belong to $\mathscr{F}$ and every element of this poset has the desidered property.
Mar
26
comment Limit as universal arrow
@LuigiM forgive me, in the first part of the answer I've got confused... I've edited to correct the mistake. :)
Feb
15
comment The functor $\mathbf{D} \rightarrow \mathbf{Prof}$ obtained by “splitting” $F : \mathbf{C} \rightarrow \mathbf{D}$ at each object of $\mathbf{D}.$
@goblin it is indeed, the part I'm referring to is the last section Distributors and generalized fibrations.
Jan
8
comment Degree of the extension $\mathbb{Q}(\zeta_3,\zeta_7)$ over $\mathbb{Q}$
@JackD'Aurizio for start since $[\mathbb Q(\zeta_7):\mathbb Q]=6$ it's not so clear why $\sqrt{-3}=Q_1+Q_2\zeta_7$ and not $Q_0+Q_1\zeta_7+\dots+Q_6 \zeta_7^6$, second it's not so clear (at least not to me) why the relation $-3=(Q_1+Q_2\zeta_7)^2$, which holds in $\mathbf Q(\zeta_7)$ should also hold in the finite field $\mathbb F$.... guess I'm a little rusty on arithmetics...
Jan
8
comment Degree of the extension $\mathbb{Q}(\zeta_3,\zeta_7)$ over $\mathbb{Q}$
@JackD'Aurizio I guess the not so easy part is why from the fact that $\sqrt{-3} \in \mathbb Q(\eta_7)$ should follow that in the finite field there is a square root of $-3$.
Jan
7
comment How to introduce type theory to newcomer
@MikeStay I've read the paper but it seems to deal with the relation between typed and untyped theories, so how does it relate to my issue here? Am I missing something?
Jan
7
comment How to introduce type theory to newcomer
@NikolajK I'm afraid they very limited knowledge: mostly simple basic programming in C.
Jan
6
comment How to introduce type theory to newcomer
@MikeStay Thanks for the link, I'm definitively going to read it.
Jan
6
comment How to introduce type theory to newcomer
Anyway I wanted to see if anyone could give me other hints in order to help me to choose one of the two solutions.
Jan
6
comment How to introduce type theory to newcomer
@cody I've take a look at some references, primarily to the Homotopy type theory book and to The seven virtues of simple type theory. The first reference doesn't clearly address my issue while the second seems to tend to the second approach (the one which takes also dependent terms).
Dec
6
comment Example of an associative binary operation, without identities or inverses.
@Bartek Yeah, but at the time I wrote the answer the OP didn't say anything about commutativity.
Nov
24
comment System of generators and surjective homomorphism
@MartinBrandenburg ops... thanks for pointing out, I'm going to edit immediately.
Nov
23
comment Homotopy Groups for Categories
I wouldn't dare to call this constuction $\pi_1$ of a category, mainly because this is structure distinguish an n-tuple of composable arrows in the category and their composite....
Nov
21
comment Why is this not a category?
A little add: if instead one consider the families $mor_{\mathbb P}(O,Q)$ of decreasing monotone functions these data do not form a category.... well not in the natural way.
Jul
17
comment Proof completion: if $Y$ is a closed term in strong nf, then $Yx$ weakly reduces to a strong nf $Z$
@RoyO. After a deep reading of the book you cited above I think I've finally found a solution to your problem, take a look and let me know if it's not clear :)
Jul
16
comment Algebras of the environment monad
@MartinBrandenburg aaaaaah I see now. I'm sorry I've misread the question, anyway since it seems that the OP seems interested I think it would better leave it....
Jul
16
comment Algebras of the environment monad
@JeffRussell yes, because $(-)^E \circ (-)^E={(-)^E}^E$ so by the isomorphism ${(-)^E}^E \cong (-)^{E \times E}$ (a.k.a. the exponential law) we get the monad structure.
Jul
15
comment Algebras of the environment monad
@MartinBrandenburg The OP asked "Is there a more natural way to describe these things?" I presented such monad as the image of the comonoid through the yoneda embedding, isn't it a different way to describe the monad?
Jul
8
comment Proof completion: if $Y$ is a closed term in strong nf, then $Yx$ weakly reduces to a strong nf $Z$
@RoyO. I'm probably a little rusty, but isn't it true that a reduction of a term has complexity less than the starting term?