Is the global section functor for cosheaves right exact? For sheaves, this functor is left exact, thus giving rise to sheaf cohomology as a right derived functor, so I was wondering if this corresponded to cosheaf homology as a left derived functor.
2026-03-26 16:03:55.1774541035
Global section functor on cosheaves
89 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 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?
Ok so the answer is yes. Follows from the gluing axiom.