Is the global sections functor for precosheaves fully exact? Or just right exact?
2026-03-26 17:30:33.1774546233
Global Section Functor exactness for Precosheaves
104 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
There are 1 best solutions below
Related Questions in HOMOLOGY-COHOMOLOGY
- Are these cycles boundaries?
- Cohomology groups of a torus minus a finite number of disjoint open disks
- $f$ - odd implies $d(f)$ - odd, question to the proof
- Poincarè duals in complex projective space and homotopy
- understanding proof of excision theorem
- proof of excision theorem: commutativity of a diagram
- exact sequence of reduced homology groups
- Doubts about computation of the homology of $\Bbb RP^2$ in Vick's *Homology Theory*
- the quotien space of $ S^1\times S^1$
- Rational points on conics over fields of dimension 1
Related Questions in SHEAF-THEORY
- Is $ X \to \mathrm{CH}^i (X) $ covariant or contravariant?
- Question about notation for Čech cohomology and direct image of sheaves in Hartshorne
- Does sheafification preserve surjectivity?
- Image of a morphism of chain complexes of sheaves via direct/inverse image functor
- Tensor of a $k[X]$ module with the structure sheaf of an affine variety is a sheaf
- Sheafy definition for the tangent space at a point on a manifold?
- Whats the relationship between a presheaf and its sheafification?
- First isomorphism theorem of sheaves -- do you need to sheafify if the map is surjective on basis sets?
- An irreducible topological space $X$ admits a constant sheaf iff it is indiscrete.
- Why does a globally generated invertible sheaf admit a global section not vanishing on any irreducible component?
Related Questions in SHEAF-COHOMOLOGY
- Question about notation for Čech cohomology and direct image of sheaves in Hartshorne
- Image of a morphism of chain complexes of sheaves via direct/inverse image functor
- Does $H^2(X_{Zar},\mathcal{O}_X^\times)=0$ for $X$ a regular scheme?
- Computing the dimension of $H^0(X, \mathcal{O}_X(D))$, where $D \subset X$ is a divisor
- Is the cohomology of a stalk the same as the stalk of the cohomology sheaf?
- If $H^i(\tilde{X}, \mathcal{F}) = 0$, then is it true that $H^i(X, \mathcal{F}) = 0$?
- Conditions on $\mathcal{F}$ such that $\chi(\mathcal{F}) = 0$ for a coherent sheaf on a curve over $k$.
- Cohomology and inverse image of divisors
- $\dim H^0(X, \mathcal{O}_D) \leq 1 + \deg D$ when $-1 \leq \deg D \leq g - 1$
- Bott vanishing from the Euler sequence
Related Questions in DERIVED-FUNCTORS
- Derived functors in the category of sheaves
- Question about $\mbox{Ext}$ groups in abelian categories
- Determining right derived functor of the left exact functor $M \to M[p]$.
- Defining contravariant left/right-exact functor with opposite category?
- Transfer modules and Weyl algebra
- Derived functors and induced functors
- Tor functor on a torsion ring
- Properties of derived functors
- Cohomology of $Hom$'s between Complexes
- When does the inverse image functor commute with internal hom?
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?
Precosheaves are just presheaves valued in the opposite category. Limits and colimits of presheaves are computed pointwise, so taking sections over any open (in particular, taking global sections) is exact, and in fact preserves all limits and colimits.