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Sep
16
revised Category of Grp is not a subcategory of Set
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Sep
16
answered Category of Grp is not a subcategory of Set
Sep
16
revised Category of Grp is not a subcategory of Set
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Sep
16
comment Given heaps $h$ and $h'$, is true that if $h \leq h'$ and $h' \leq h$, then $h = h'$?
No. This is something very special to $\mathbf{Set}$, and the inverse operation requires the axiom of replacement.
Sep
16
answered Given heaps $h$ and $h'$, is true that if $h \leq h'$ and $h' \leq h$, then $h = h'$?
Sep
16
revised Given heaps $h$ and $h'$, is true that if $h \leq h'$ and $h' \leq h$, then $h = h'$?
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Sep
16
comment Is it true that a dihedral group is nonabelian?
You need to explain why the inequality holds.
Sep
16
revised When does a left adjoint between Heyting algebras preserve 1?
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Sep
15
comment Are small categories large?
Are finite sets countable? Sometimes they are, sometimes they aren't...
Sep
15
comment Right exactness on a dense subcategory
Take $\mathcal{J}$ to be the parallel pair category and the finite discrete categories, I suppose. I don't know what the theoretical condition amounts to in practice. The case of locally presentable + compact objects is much simpler.
Sep
15
comment Examples of affine schemes
Irreducible algebraic curves with the Zariski topology are not very interesting as topological spaces. Over a given algebraically closed base field, they are all homeomorphic to a space where all but one point is closed, and the closed sets are precisely the finite sets of closed points.
Sep
15
comment Right exactness on a dense subcategory
I added a theoretical condition for the general case.
Sep
15
revised Right exactness on a dense subcategory
added 2152 characters in body
Sep
15
comment Computing easy direct limit of groups
At first I read $\langle m, k \rangle$ as the subgroup generated by $m$ and $k$...
Sep
15
answered Right exactness on a dense subcategory
Sep
14
comment Is there a topos in which the natural numbers object are the finite dimensional vector spaces?
Any countable set can be an NNO in $\mathbf{Set}$ – NNOs are only unique up to unique isomorphism. Please learn some category theory.
Sep
14
comment Is there a topos in which the natural numbers object are the finite dimensional vector spaces?
But then the modified question is boring: $\mathbf{Set}$ is such a topos!
Sep
14
answered Explicit construction of a initial object in a topos
Sep
14
revised Explicit construction of a initial object in a topos
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Sep
14
comment Explicit construction of a initial object in a topos
I suppose you are referring to the textbook of Mac Lane and Moerdijk? You should be more explicit about what definition of topos you are taking for the purpose of this question.