Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory internal-categories k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorBaptiste
   • CommentTimeOct 6th 2017
   • PermaLink
   Author: Baptiste
   Format: MarkdownItexHello, In the (infinity,1)-functor page, in part [Properties](https://ncatlab.org/nlab/show/%28infinity%2C1%29-functor#properties), there is a Theorem. Some notation is introduced in it, [C^op,KanCplx]°, but instead [C^op,sSet]° is used in the statement. Is the statement incorrect? Also, I guess it would be nice to add a reference for this Theorem. Does anyone have one?

   Hello,

   In the (infinity,1)-functor page, in part Properties, there is a Theorem. Some notation is introduced in it, [C^op,KanCplx]°, but instead [C^op,sSet]° is used in the statement. Is the statement incorrect?

   Also, I guess it would be nice to add a reference for this Theorem. Does anyone have one?

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeOct 6th 2017
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexYes, this theorem statement is a bit confused. The fibrant and cofibrant objects *are* all valued in Kan complexes, but a consistent notation should be used. Also the text says we have an equivalence of $\infty$-groupoids, but the displayed equation is an equivalence between $(\infty,1)$-categories. For a reference, if you follow enough links you can find a citation to Lurie at [[(infinity,1)-category of (infinity,1)-functors]] (models).

   Yes, this theorem statement is a bit confused. The fibrant and cofibrant objects are all valued in Kan complexes, but a consistent notation should be used. Also the text says we have an equivalence of $\infty$-groupoids, but the displayed equation is an equivalence between $(\infty,1)$-categories.

   For a reference, if you follow enough links you can find a citation to Lurie at (infinity,1)-category of (infinity,1)-functors (models).

3. • CommentRowNumber3.
   • CommentAuthorBaptiste
   • CommentTimeOct 9th 2017
   • PermaLink
   Author: Baptiste
   Format: MarkdownItexThank you. I understand the statement in the reference to Lurie. I'm not making the edit to clarify the entry under discussion, because I'm not sure how to do it. I don't think it's a good idea, in a statement, to mix concrete models for $(\infty,1)$-categories (such as quasicategories, at the beginning of the statement) and then general $(\infty,1)$-notions that should in principle existe for any model (such as $(\infty,1)$-functor later on). Here the final equivalence in the statement seems to live in the world of simplicial categories. So what should be done?

   Thank you.

   I understand the statement in the reference to Lurie.

   I’m not making the edit to clarify the entry under discussion, because I’m not sure how to do it. I don’t think it’s a good idea, in a statement, to mix concrete models for $(\infty,1)$-categories (such as quasicategories, at the beginning of the statement) and then general $(\infty,1)$-notions that should in principle existe for any model (such as $(\infty,1)$-functor later on). Here the final equivalence in the statement seems to live in the world of simplicial categories. So what should be done?

4. • CommentRowNumber4.
   • CommentAuthorMike Shulman
   • CommentTimeOct 9th 2017
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexThis theorem is all about particular models, I don't think there is any part of it that makes sense model-independently.

   This theorem is all about particular models, I don’t think there is any part of it that makes sense model-independently.

5. • CommentRowNumber5.
   • CommentAuthorMike Shulman
   • CommentTimeOct 16th 2017
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexI made the least invasive edit I could think of that I think makes the statement true and all notations defined.

   I made the least invasive edit I could think of that I think makes the statement true and all notations defined.

6. • CommentRowNumber6.
   • CommentAuthorBaptiste
   • CommentTimeOct 23rd 2017
   • PermaLink
   Author: Baptiste
   Format: MarkdownItexThanks. It looks better indeed. I understand that this theorem is about particular models; actually, it seems to be about the particular model of quasi-categories. That is why I believe the statement should end by Then we have an equivalence of **quasi-categories** etc. But it is a minor point, I guess.

   Thanks. It looks better indeed.

   I understand that this theorem is about particular models; actually, it seems to be about the particular model of quasi-categories. That is why I believe the statement should end by

   Then we have an equivalence of quasi-categories etc. But it is a minor point, I guess.