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Oct
2
answered Equivalent Conditions for left-adjoint-left-inverse
Oct
2
answered Equivalence of categories $\Pi_1:\mathbf{K^1_{CW,*}}\to \mathbf{Grp}$
Oct
2
comment Equivalence of categories $\Pi_1:\mathbf{K^1_{CW,*}}\to \mathbf{Grp}$
What? The higher homotopy groups $\pi_n$ have a perfectly good classical definition not involving any $n$-groupoids.
Oct
2
answered Computation of adjoint functors (sheafification)
Oct
2
comment Equivalent Conditions for left-adjoint-left-inverse
Just do it by hand. It's the usual transport-of-structure argument. (For example, if $G$ is a group and $X$ is a set such that $X \cong G$, then there is a group structure on $X$ making the given bijection a group isomorphism.)
Oct
1
comment Computation of adjoint functors (sheafification)
Look up the Grothendieck plus construction.
Oct
1
comment Computation of adjoint functors (sheafification)
Yes, you can compute adjoints in terms of limits/colimits. In fact that is what the adjoint functor theorem says.
Sep
30
awarded  Explainer
Sep
29
comment Endomorphisms of constant sheaves on connected spaces
On 1: Your interpretation and proof are correct.
Sep
27
comment Proving that some property on a chain complex of groups implies isomorphism between direct sums of these groups.
It's easy enough to unpack the proof Martin has outlined, if you really have to.
Sep
25
comment Continuity of multiplication in algebras over $\mathbb{C}$
@copper.hat There are two kinds of multiplication. You are talking about multiplication by a scalar, the OP is asking about multiplication of two elements.
Sep
25
answered What is the 'type' of a natural transformation
Sep
25
comment Continuity of multiplication in algebras over $\mathbb{C}$
More to the point, how do you define topological algebra? A typical definition requires continuity of multiplication.
Sep
24
awarded  Notable Question
Sep
24
comment Why is there no theory of $G$-ic varieties, for linear algebraic groups $G$?
The algebraic torus is not a torus, however.
Sep
24
comment Birkhoff's completeness theorem
It is not really possible to give a good example of a proof of an equation that uses first-order logic: after all, Birkhoff's theorem implies that any use of first-order logic can be eliminated. Of course, this only makes sense in a setting where all the axioms are equations.
Sep
24
comment Quasi-isomorphism from “almost acyclic” complex to its homology
It is not unreasonable to interpret "$X$ is quasi-isomorphic to $Y$" as "there is a zigzag of quasi-isomorphisms from $X$ to $Y$".
Sep
23
comment Can an open subset of an affine variety and the variety itself have isomorphic rings of regular functions?
How about $\mathbb{A}^2$ and $\mathbb{A}^2 \setminus \{ 0 \}$?
Sep
23
comment Hyperplanes as dual projective spaces
Think about a necessary and sufficient condition for two linear functionals to define the same hyperplane.
Sep
22
comment Is projection $\mathbb{A}^2 \to \mathbb{A}$ finite?
Well, $k [x, y]$ is not a finite $k [x]$-algebra.