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5h
comment The coproduct of a family of objects of a Preorder (seen as a category)
Yes, it is the least upper bound. The proof is the same, except for some fiddling with equality.
2d
comment is axiom of powers required?
Is your collection of singletons actually a set? You can only take unions over sets.
2d
answered What is the relationship between the path-loop space fibration and path induction?
2d
comment What is the relationship between the path-loop space fibration and path induction?
Well, based path induction is more or less the statement that the space $P X$ is contractible (plus some auxiliary facts about contractible spaces). But $\Omega X$ doesn't come into it.
2d
awarded  Favorite Question
May
22
comment Is it possible to develop differential geometry without points?
Locales are like topological spaces, not manifolds. Besides, every Hausdorff space is sober, so the category of Hausdorff spaces embeds as a full subcategory of the category of locales.
May
21
comment Is $\coprod \subseteq \prod$ true in any (complete cocomplete) Abelian category?
Well, no: if it were true then the dual result would force it to be an isomorphism, which is absurd.
May
20
comment left adjointable functors
Well, there is also "It is a left half", which sounds less grammatical than "It is the left half". My point is that the grammaticality of "$F$ is a left adjoint" cannot be determined by general arguments.
May
20
comment left adjointable functors
Your objection is invalid. For example, "He is a father" is perfectly grammatical as a sentence.
May
20
comment Is every reduced $k$-algebra all of whose residue fields are $k$ finitely generated?
Sorry, I misremembered. Your hypothesis implies that $A$ is zero-dimensional.
May
20
comment left adjointable functors
For me, "$F$ is left adjointable" sounds more like "$F$ has a left adjoint", which is the opposite of "$F$ is a left adjoint".
May
20
comment Relation between Noether's one-sided ideals and Polish notation?
There is no relation with Polish notation. In fact, Polish notation makes the relationship more obscure: the difference in question is between $r \, a \, b \, {+} \, {\times}$ and $a \, b \, {+} \, r \, {\times}$.
May
20
comment Intuitionistically, are these inequivalent? $P \rightarrow Q,\; \neg Q \rightarrow \neg P,\; P \wedge \neg Q \rightarrow \bot,\; \neg P \vee Q$
$\lnot Q \to \lnot P$ and $P \land \lnot Q \to \bot$ are equivalent. The rest are different.
May
19
comment Geometrically, why do line bundles have inverses with respect to the tensor product?
For me the problem comes even earlier: what is the geometric significance of the tensor product of line bundles?
May
19
comment Regarding Espace Etale of a presheaf, is $\bar s$ an open map?
Yes, sections of espaces étalés are always open embeddings.
May
19
answered Is any reflector from a presheaf category $PSh(K)$ to a topos $C$ necessarily left exact?
May
19
comment An injective morphism between varieties that is not an immersion
Sure. Take the projective closures of $X$ and $Y$.
May
19
revised An injective morphism between varieties that is not an immersion
added 267 characters in body
May
19
answered An injective morphism between varieties that is not an immersion
May
18
answered Inclusions of CW-complexes are cofibrations.