Reputation
Next tag badge:
93/100 score
27/20 answers
Badges
2 53 128
Newest
 Enlightened
Impact
~368k people reached

May
5
answered Which axiom of set theory does this formula represent ? Why?
May
5
revised Which axiom of set theory does this formula represent ? Why?
edited tags
May
5
answered Are sections of vector bundles $E\to X$ over schemes necessarily closed embeddings?
May
5
comment what is the precise definition of a morphism defined over $k$?
Well, instead of thinking about automorphisms, first generalise to morphisms between arbitrary varieties over $k$. Then specialise to affine varieties and use the correspondence with $k$-algebras.
May
5
comment Is the diagonal map $\mathbb{C} \to \prod_{i=1}^\infty \mathbb{C}$ an etale map of rings?
@yogeshmore No, it is not. A morphism of affine schemes is étale if and only if the corresponding ring homomorphism is étale.
May
5
answered Is the skeleton-coskeleton adjunction $sSet$-enriched?
May
4
comment Covariant and Contravariant Functor of Fixed Set Question - Category of Sets
The question is imprecise. After all, the formulae $X \mapsto X^A$ and $X \mapsto A^X$ do not specify what happens to morphisms. The point is to define actual functors whose object parts are as specified – so there's really nothing much to it at all.
May
2
answered when a presheaf is a sheaf
May
2
comment Classifying space infinite totally ordered set contractible
@NajibIdrissi $\omega_1$ has a bottom element, so its nerve is contractible (in the strong sense). More generally, any category with an initial object has contractible nerve.
May
1
accepted Positive and negative logical connectives
May
1
comment Adjunction between topological and simplicial presheaf categories
$\mathcal{C}^\Delta$ is not good notation, so I will write $\mathcal{D}$ instead. It is not hard to see that $\mathbf{Top} \to \mathbf{sSet}$ induces a functor sending topologically enriched functors $\mathcal{C} \to \mathbf{Top}$ to simplicially enriched functors $\mathcal{D} \to \mathbf{sSet}$, but I don't see any candidate for a left adjoint. (Actually, the only functors going the other way that I can think of are either constants or factor through the homotopy category.)
May
1
comment Tor Functor Commutes with Direct Limits
Classically, "direct limit" means "colimit of a directed diagram". In particular, they are filtered colimits.
Apr
30
comment Can I define a predicate over a set and use it in the definition of another one?
Are you trying to work in a specific axiomatic set theory?
Apr
30
comment How to understand cocategories
For any $\mathcal{C}$ with pullbacks, cocategories in $\mathcal{C}$ are the same as functors $\mathcal{C} \to \mathbf{Cat}$ whose composites with $\operatorname{ob}, \operatorname{mor} : \mathbf{Cat} \to \mathbf{Set}$ are representable. Such functors are not so common, but there are a few examples, e.g. the left and right adjoints of $\operatorname{ob} : \mathbf{Cat} \to \mathbf{Set}$.
Apr
30
comment Characterization of epic morphisms in the category of rings.
See this question.
Apr
30
comment Points of scheme with residue field $k$ vs $k$-point
That's not possible when all the morphisms are $k$-morphisms.
Apr
29
comment Choice of a skeleton
Actually, in my mind, a skeleton is not just a full subcategory but also equipped with a quasi-inverse to the inclusion. At any rate, all you need is a sufficiently strong axiom of choice (and the law of excluded middle).
Apr
29
comment Is $S^1 \times S^1$ really a torus?
The torus has many (Riemannian) metrics. One of them is even flat!
Apr
29
revised Is there a more general obstruction to the existence of moduli spaces than the existence of automorphisms?
deleted 15 characters in body
Apr
29
revised $\{P\}^-$ notation in Algebraic Geometry
edited tags