<em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

    <em id="zlul0"></em>

      <dl id="zlul0"></dl>
        <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
        <em id="zlul0"></em>

        <div id="zlul0"><ol id="zlul0"></ol></div>

        Stack Exchange Network

        Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

        Visit Stack Exchange

        For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.

        5
        votes
        1answer
        60 views

        Inductive folk model structure on strict ω-categories

        There is a paper of Lafont, Metayer, and Worytkiewicz [1] that constructs a model structure on the category of strict $\omega$-categories that they call the folk model structure. This model structure ...
        7
        votes
        0answers
        142 views

        Testing for equivalences of $\infty$-categories on strictifications?

        It is in general not too hard to show that maps between finite $CW$-complexes/finite simplicial sets are homotopy equivalences. Question : Can we do something similar for: quasi-categorical ...
        3
        votes
        0answers
        145 views

        Tannaka duality for $DG$ indschemes

        In Lurie's paper on Tannaka duality for geometric stacks he proves that there is a natural isomorphism $$\operatorname{Hom}(X,Y) \cong \operatorname{Hom}(\mathbf{QC}(Y), \mathbf{QC}(X)$$ where $X$ and ...
        3
        votes
        1answer
        115 views

        Cellularity of anodyne extensions?

        Are the anodyne extensions of simplicial sets always relative cell complexes of horn inclusions? (i.e. there is no need to consider retracts) If not, is there a known counterexample? Similarly, does ...
        20
        votes
        0answers
        196 views

        Explicit Left Adjoint to Forgetful Functor from Cartesian to Symmetric Monoidal Categories

        There is a forgetful functor from the category of (small) Cartesian monoidal categories (a symmetric monoidal category in which the tensor product is given by the categorical product) to the category ...
        8
        votes
        2answers
        282 views

        What is a spectrum object in $\infty$-topoi?

        For any spectrum $E$, there is a "discrete" topos spectrum $(Spaces / E_n)_n$. And I believe any topos spectrum is a localization of a "discrete" one. Are there any "non-discrete" topos spectra? To ...
        3
        votes
        0answers
        130 views

        Is $Ind(N_{dg}(\mathcal{C})) \simeq N_{dg}(Ind(\mathcal{C}))$ for an additive category $\mathcal{C}$?

        Let $\mathcal{C}$ be an additive category and let $N_{dg}(\mathcal{C})$ be the differential graded nerve of the differential graded category $Ch(\mathcal{C})$. This is a stable $\infty$-category. ...
        10
        votes
        0answers
        212 views

        What are the monomorphisms of ($\infty$-)toposes?

        There are standard notions of "surjections" and "embeddings" of toposes. However, not every surjection is an epimorphism, and not every regular monomorphism is an embedding. (EDIT: as Alexander ...
        11
        votes
        1answer
        251 views

        Are there continua in $\infty$-topoi?

        If topology were invented for algebraic geometry or logic, in ignorance of Euclidean space, we might reasonably regard connected compact Hausdorff spaces as pathological, or even doubt their existence....
        3
        votes
        1answer
        216 views

        Why must the essential image break the principle of equivalence?

        I'm having trouble understanding why the "essential image" is defined the way it is. The nlab article gives the following definition: (A concrete realization of) the essential image of a functor $...
        9
        votes
        0answers
        198 views

        Homotopy pullbacks of simplicial sets; Joyal vs Kan-Quillen model structures

        I am interested in comparison of homotopy pullback squares in the category of simplicial sets with respect to Joyal' model structure and Quillen's one. Suppose we are given a (strict) pullback square ...
        8
        votes
        1answer
        395 views

        Spectral and derived deformations of schemes

        I'd like to understand how ordinary schemes deform or lift to spectral and derived schemes in two basic examples as well as what the structure of the space of deformations in general is. Let $S = (X, ...
        35
        votes
        2answers
        760 views

        What parts of the theory of quasicategories have been simplified since the publication of HTT?

        It has been almost ten years since Lurie published Higher Topos Theory, where (following Joyal and probably others) he set up foundations for higher category theory via quasicategories. My impression ...
        7
        votes
        4answers
        374 views

        Localization of $\infty$-categories

        In ordinary category theory, the localization $C[S^{-1}]$ at a class of morphisms $S$ (with possibly some assumptions on $S$) is a category $C[S^{-1}]$ together with a map $L:C \to C[S^{-1}]$ such ...
        3
        votes
        0answers
        174 views

        Cell structure on $B\mathbb{G}$ and the bar resolution of $\mathbb{G}$

        Consider $\mathbb{G}$, which can be viewed as a group, as well as a 2-group. (For example, given a short exact sequence $$ 1 \to BG_2 \to \mathbb{G} \to G_1 \to 1 $$ and the fiber sequence: $$ B^2G_2 ...

        15 30 50 per page
        山西福彩快乐十分钟
          <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

          <em id="zlul0"></em>

            <dl id="zlul0"></dl>
              <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
              <em id="zlul0"></em>

              <div id="zlul0"><ol id="zlul0"></ol></div>
                <em id="zlul0"></em><dl id="zlul0"><menu id="zlul0"></menu></dl>

                <em id="zlul0"></em>

                  <dl id="zlul0"></dl>
                    <div id="zlul0"><tr id="zlul0"><object id="zlul0"></object></tr></div>
                    <em id="zlul0"></em>

                    <div id="zlul0"><ol id="zlul0"></ol></div>