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Sep
2
revised Tensor product of injective ring homomorphisms
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Sep
2
revised Tensor product of injective ring homomorphisms
added 897 characters in body
Sep
2
comment Étalé space for sheaf of sections of a fiber bundle
There is no nice description, because the espace étalé itself is not nice. For instance, the one corresponding to the sheaf of smooth functions on a smooth manifold is not even Hausdorff.
Sep
2
answered Is a pre-additive structure on a category $\mathcal{C}$ necesarrily unique?
Sep
2
comment Tensor product of injective ring homomorphisms
Related question on MO.
Sep
2
comment Colimits in the category of “sets with partial mappings”
Well, having a right adjoint, the forgetful functor is a left adjoint and therefore preserves colimits. It's as simple as that.
Sep
2
answered map between classifying spaces induced by group homomorphism
Sep
2
revised Tensor product of injective ring homomorphisms
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Sep
2
comment Tensor product of injective ring homomorphisms
Hmmm, yes. So the only thing that can go wrong is that some nilpotent goes to zero in $A \otimes_R B$ but not in $A$ or $B$. Maybe there is an example after all.
Sep
1
comment Is there a minimal axiomatization of ZFC?
Take the theory with countably many constants $c_i$ and axioms $c_i \ne c_j$ for $i < j$. Then that axiomatisation is minimal, no? The same argument works for both the finite and infinite case.
Sep
1
revised Tensor product of injective ring homomorphisms
edited tags
Sep
1
answered Tensor product of injective ring homomorphisms
Sep
1
revised Why is the Leibniz rule a sufficient ingredient in the construction of the tangent space?
edited tags; edited title
Sep
1
comment Definition of “contradiction” and use of the term for “⊥”
It is convenient to have $\bot$ as a propositional constant. If you don't like it, you can replace it with any of your favourite contradictions – e.g. $0 = 1 \land 0 \ne 1$ – they are all logically equivalent. In other words, $\bot$ is the abstract contradiction.
Sep
1
answered $G$ conservative iff counit components are extremal epi.
Aug
31
comment What is the right category in which to think of adjoints?
Actually, I think the convention is that a functor $\mathcal{C}^\mathrm{op} \times \mathcal{D} \to \mathbf{Set}$ is a profunctor from $\mathcal{D}$ to $\mathcal{C}$. This is certainly the case on the cited page. A mnemonic for remembering this: the category of profunctors from $\mathcal{D}$ to $\mathcal{C}$ is equivalent to the category of left adjoints $[\mathcal{D}^\mathrm{op}, \mathbf{Set}] \to [\mathcal{C}^\mathrm{op}, \mathbf{Set}]$, at least when $\mathcal{C}$ and $\mathcal{D}$ are small.
Aug
31
comment Closed model categories in the sense of Quillen [1969] vs the modern sense
No. I'm not looking for a reference.
Aug
31
comment Sheaf associated to sheaf on basis
Verifying the stalks are the same is somewhat non-trivial, but the bigger problem is that a sheaf is not determined by its stalks alone. See here.
Aug
31
comment Two questions on kernels
Sorry, you need to assume $k'$ is a monomorphism.
Aug
31
revised Two questions on kernels
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