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Dec
15
answered Example of a function between boolean lattices that preserves $(\top,\bot,\wedge,\vee)$ but not complements.
Dec
15
comment axioms of equality
That's the converse, also known as Leibniz's law.
Dec
15
answered axioms of equality
Dec
15
comment How or why does intutionistic logic proof negations from within the theory, constructively?
@NickKidman To say that a function that cannot be called is not a function is absurd. That's like saying that dead code in a program is not really code.
Dec
14
comment How or why does intutionistic logic proof negations from within the theory, constructively?
That's just your opinion, moulded by years of studying classical mathematics. Ask someone not exposed to mathematics what a proof of "A or B" should be, and you will surely be told it is either a proof of A or a proof of B – exactly as in intuitionistic logic.
Dec
13
comment How does this definition capture the intuitive notion of an algebra?
It's not quite the comma category $(T \downarrow \mathcal{E})$, but it is a full subcategory thereof.
Dec
13
comment Derived functors and coboundary operator
Right. But the point is that the bar complex comes from a particular projective resolution, not general nonsense!
Dec
13
comment Derived functors and coboundary operator
I'm not convinced they can be constructed like that in general. For instance, the bar complex for group cohomology comes from taking a projective resolution of the trivial module $\mathbb{Z}$, not an injective resolution.
Dec
13
comment $A$-points of a fiber of a morphism of schemes over $k$
Do you understand fibre products in, say, $\mathbf{Top}$ or any other conventional setting?
Dec
13
comment $A$-points of a fiber of a morphism of schemes over $k$
They are essentially the $A$-points of $X$ that lie over $y$ – but the latter condition is still something that needs to be imposed separately.
Dec
12
comment Derived functors and coboundary operator
Are you trying to avoid the standard construction via injective resolutions?
Dec
12
comment Why are proofs written in first person plural? Were they ever written differently?
Hodges writes in the preface of [Model theory]: ‘I’ means I, ‘we’ means we.
Dec
12
comment Derived functors and coboundary operator
Right derived functors are not differentials. What do you mean?
Dec
11
comment Is there always an injective map from a space in its dual space?
Hahn and Banach are two different people....
Dec
11
comment Why is the Cech nerve $C(U)$ of a surjective map $U\to X$ weakly equivalent to $X$?
Factor the map as a surjection followed by an inclusion; the Čech nerve of the surjection part is the same as the Čech nerve of the original map.
Dec
11
comment Cardinality of the set of all well formed formula in propositional logic?
Well, write it as a countable union of countable sets...
Dec
11
answered Why is the Cech nerve $C(U)$ of a surjective map $U\to X$ weakly equivalent to $X$?
Dec
10
revised Right adjoint functor
edited tags
Dec
10
answered Can natural transformations be made into functors in this way?
Dec
9
comment Is the category of chain complexes complete and cocomplete in small?
Yes, it does. They are computed degreewise.