In this remark, Lurie states that applying proposition HTT 4.3.2.15 twice, we deduce that $\theta$ is a kan fibration.
How is this assertion deduced?
2026-03-26 08:15:06.1774512906
HA, 1.1.1.7, Lurie
123 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 HOMOTOPY-THEORY
- how to prove this homotopic problem
- Are $[0,1]$ and $(0,1)$ homotopy equivalent?
- two maps are not homotopic equivalent
- the quotien space of $ S^1\times S^1$
- Can $X=SO(n)\setminus\{I_n\}$be homeomorphic to or homotopic equivalent to product of spheres?
- Why do $S^1 \wedge - $ and $Maps(S^1,-)$ form a Quillen adjunction?
- Is $S^{n-1}$ a deformation retract of $S^{n}$ \ {$k$ points}?
- Connection between Mayer-Vietoris and higher dimensional Seifert-Van Kampen Theorems
- Why is the number of exotic spheres equivalent to $S^7,S^{11},S^{15},S^{27}$ equal to perfect numbers?
- Are the maps homotopic?
Related Questions in SIMPLICIAL-STUFF
- Homotopy type of simplicial complexes
- $\Pi_f$ for a morphism $f$ between simplicial sets
- Trouble with changing the fractions into matrix-vector from
- 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)
- The choice of cofibrant approximation is contractible
- Do Homotopy limits commute with right Quillen functors
- Necessary conditions for a Reedy fibrant diagram
- $\infty$-categories definition disambiguation
- For simplicial abelian group quotient map to the quotient chain complex is homotopy equivalence.
Related Questions in HIGHER-CATEGORY-THEORY
- Quillen equivalence between sSet (Joyal's model structure) and sSetCat (Bergner's one)
- What is an intuitive Geometrical explanation of a "sheaf?"
- $\infty$-categories definition disambiguation
- Applications of $\infty$-categories
- Simplicial categories and simplicial objectcs. HTT Remark 1.1.4.2
- $n$-categories and associahedrons.
- Weak notion of equivalence in a category
- The $2$-category of monoids
- Higher homotopy groups in terms of the fundamental groupoid
- Pseudolimits equivalent to limits
Related Questions in STABLE-HOMOTOPY-THEORY
- Shift in a stable $\infty$-category
- Reference for spectra theory (in topology)
- Invariant ideals of Hopf algebroid
- Why is the $J$-homomorphism an isomorphism for $n=1$?
- Equality of Hom groups via 5 lemma
- Who proved that $\pi_{n+1}(S^n) \cong \mathbb{Z}/2\mathbb{Z}$ for $n\geq 3$?
- Why Bousfield localization preserves homotopy pull-backs?
- Understanding Adams spectral sequence and Pontryagin-Thom isomorphism intuitively
- Loops Infinity of a spectrum
- Why is the map from a wedge to a product induces isomorphisms between stable homotopy groups
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?