Here in Hovey's book on Model Categories in as opposed to errata there is already injective in the lemma 2.2.8. The errata says injective and not projective. Also I wonder what is $A$ in $A\to Q$ there.
2026-03-27 16:21:12.1774628472
Injectivity or projectivity criterion in modules and model categories
30 Views Asked by user175304 https://math.techqa.club/user/user175304/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 MODULES
- Idea to make tensor product of two module a module structure
- $(2,1+\sqrt{-5}) \not \cong \mathbb{Z}[\sqrt{-5}]$ as $\mathbb{Z}[\sqrt{-5}]$-module
- Example of simple modules
- $R$ a domain subset of a field $K$. $I\trianglelefteq R$, show $I$ is a projective $R$-module
- $S_3$ action on the splitting field of $\mathbb{Q}[x]/(x^3 - x - 1)$
- idempotent in quiver theory
- Isomorphism of irreducible R-modules
- projective module which is a submodule of a finitely generated free module
- Exercise 15.10 in Cox's Book (first part)
- direct sum of injective hull of two modules is equal to the injective hull of direct sum of those modules
Related Questions in PROJECTIVE-MODULE
- $R$ a domain subset of a field $K$. $I\trianglelefteq R$, show $I$ is a projective $R$-module
- projective module which is a submodule of a finitely generated free module
- Flat modules over a PID
- Projectivity of a module
- Proving a module is projective.
- Proving a specific module is projective.
- $M\otimes_A N\cong A$ implies $M$ is left $A$-projective?
- Proof of equivalence of two definitions of a projective module
- Problem based on Projective and Injective Module
- Splitting two exact sequences in a compatible way
Related Questions in INJECTIVE-MODULE
- direct sum of injective hull of two modules is equal to the injective hull of direct sum of those modules
- injective hull of a ring that is not integral domain
- Decomposition of injective modules over polynomial rings
- Problem based on Projective and Injective Module
- Example of reduced module
- Injective object in the category of projective systems of $R$-modules.
- Injective Linear Transformation $K[x]_{\leq 4}\rightarrow V$
- For $d\mid m$, $\mathbb{Z}/d\mathbb{Z}$ is not an injective $\mathbb{Z}/m\mathbb{Z}$-module when some prime divides $d$ and $\frac{m}{d}$
- $\mathbb{Q}_{\mathbb{Z}}$ is an injective hull of $\mathbb{Z}$
- Element in a finitely generated torsion module on a PID with smallest non-zero annihilator
Related Questions in MODEL-CATEGORIES
- Why do $S^1 \wedge - $ and $Maps(S^1,-)$ form a Quillen adjunction?
- In what sense are (co)fibrant replacements "better"?
- A fibration $p : E \rightarrow X$ is trivial iff $p$ is a homotopy equivalence
- Quillen equivalence between sSet (Joyal's model structure) and sSetCat (Bergner's one)
- Definiton of the beta in Lurie's HTT
- The choice of cofibrant approximation is contractible
- Do Homotopy limits commute with right Quillen functors
- The cofibration from the $\textbf{Top}$'s model category
- Necessary conditions for a Reedy fibrant diagram
- How far are functors valued in Ho(Cat) from pseudofunctors?
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?