This is probably a rather obvious question (either obviously true or wrong). Given a presheaf on the category of schemes that satisfies descent with respect to some site. If we sheafify the presheaf with respect to another site, then does it preserve its sheaf property with respect to the first site?
2026-03-25 17:22:46.1774459366
Does sheafifying with respect to a new site destroy the already existent descent properties?
59 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in CATEGORY-THEORY
- (From Awodey)$\sf C \cong D$ be equivalent categories then $\sf C$ has binary products if and only if $\sf D$ does.
- Continuous functor for a Grothendieck topology
- Showing that initial object is also terminal in preadditive category
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- What concept does a natural transformation between two functors between two monoids viewed as categories correspond to?
- Please explain Mac Lane notation on page 48
- How do you prove that category of representations of $G_m$ is equivalent to the category of finite dimensional graded vector spaces?
- Terminal object for Prin(X,G) (principal $G$-bundles)
- Show that a functor which preserves colimits has a right adjoint
- Show that a certain functor preserves colimits and finite limits by verifying it on the stalks of sheaves
Related Questions in SCHEMES
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- Do torsion-free $\mathcal{O}_X$-modules on curves have dimension one?
- $\mathbb{C}[x,y]$ is the sections of Spec $\mathbb{C}[x,y]$ minus the origin?
- Finitely generated $k-$algebras of regular functions on an algebraic variety
- Is every open affine subscheme of an algebraic $k-$variety an affine $k-$variety?
- Scheme Theoretic Image (Hartshorne Ex.II.3.11.d)
- Is this a closed embedding of schemes?
- Adjunction isomorphism in algebraic geometry
- Closed connected subset of $\mathbb{P}_k^1$
- Why can't closed subschemes be defined in an easier way?
Related Questions in GROTHENDIECK-TOPOLOGIES
- Minimal site that induces a stack from a psuedofunctor
- Coincidence of classical notion of covering in classical topology and covering sieve in grothendieck topology
- Locality in Grothendieck Topologies
- "Coverings" and "covers" in Grothendieck topologies
- Grothendieck sites based on large categories?
- The étale topos is coherent: does the scheme need to be quasicompact?
- Is it known that the etale topology on schemes does not have cd structure?
- Map from schemes to stacks
- What changes in the sheaf theory of topological spaces with the "étale topology"?
- Grothendieck Universe
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?