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May
1
comment Is a closed set in the subspace topology always closed in the space topology?
More easily $Y$ is closed in its own topology but it usually is not closed in $X$.
May
1
answered Can Lagrange's Theorem for algebraic structure apply here?
Apr
30
comment Can Lagrange's Theorem for algebraic structure apply here?
@KatherineWong would give a little of context? There are quite different ways to prove this statements depending on your background knowledge. What do you know? What theorems can you use?
Apr
24
comment Subcategory of category of Module satisfies SSA?
@henry answer 2 applies to every category of modules. About answer 1 it seems that the same argument could be applied to the case of $\mathbb Q[x]$-modules (direct product of infinite free modules, copies of $\mathbb Q[x]$, need not to be free). Note that $\mathbb Q[x]$ is an infinite dimensional $\mathbb Q$-algebra.
Apr
23
answered Subcategory of category of Module satisfies SSA?
Apr
23
comment Subcategory of category of Module satisfies SSA?
What is exactly the question in 2? Are you asking if the inclusion functor verifies the solution set condition?
Apr
18
answered Relation between Cartesian closed category and Lambda Calculus
Apr
18
comment Relation between Cartesian closed category and Lambda Calculus
Of course my previous comment applies if by lambda-calculus you mean the untyped lambda-calculus. Did you meant symply typed lambda-calculus instead?
Apr
18
comment Relation between Cartesian closed category and Lambda Calculus
I think that question 2) is ill posed: lambda calculus cannot express the structure of a cartesian closed category. On the other hand you can interpret lambda calculus in a cartesian closed category.
Apr
16
answered How to prove this Category Theory theorem?
Apr
16
comment How to prove this Category Theory theorem?
@user158083 Give me some time, I'll write another answer where I'll address this question.
Apr
15
comment How to prove this Category Theory theorem?
Feel free to ask if you need additional clarification or details.
Apr
15
comment How to prove this Category Theory theorem?
@user158083 I've made some changes hopefully they'll get you a better understanding of where the problem lies. Meanwhile I've also add a counter-example to one of the wrong implications, finding a counter-example to the other implication it's a little harder since it would require to find a functor $H$ which has a left adjoint and a functor $F$ whose object part agree with such left adjoint, but the arrow part does not.
Apr
15
revised How to prove this Category Theory theorem?
Make some improvements
Apr
15
comment How to prove this Category Theory theorem?
If you'll find stuck in finding the counter-example feel free to ask. I'll try to post them as soon as possible, but I believe that it would more instructive if you tried to find them by yourself first.
Apr
15
answered How to prove this Category Theory theorem?
Apr
9
revised Free monoidal category over a set
Added specifications
Apr
9
comment Free monoidal category over a set
@user329838 are you referring to the first line in the answer? If that's the case they are similar because in strict categories you don't simply require that the $n$-fold product of objects to be equal, you also require that associators and left and right unit are identities. In your question you didn't add such a requirement so the free-strict-category is not exactly the category you describe either.
Apr
8
comment Free monoidal category over a set
Just a speculation.
Apr
8
comment Free monoidal category over a set
If you work with $1$-categories I guess so. Nonetheless if you instead want to consider the $2$-category of monoidal categories and monoidal functor between them.... well I think the story could be different: I think (if not entirely sure) that in that case the two categories should be equivalent, but then you shouldn't have a unique functor $\bar f$, only one unique up to natural isomorphism.