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

(0 1)-category-theory 2-category 2-category-theory 2-monad abelian-categories accessible adjoint algebra algebraic algebraic-geometry analysis arithmetic beauty book bug bundle categories category category-theory chern-simons-theory cohesion cohesive-homotopy-type-theory cohomology combinatorics complex-geometry conference connection constructive constructive-mathematics cosmology database deformation-theory descent differential differential-cohomology differential-geometry duality enriched enriched-category-theory enrichment examples factorization-system fiber fibration forms foundation foundations functional-analysis functor galois-theory gauge-theory gebra general topology geometric geometric-quantization geometry gravity group-theory higher higher-algebra higher-category-theory higher-geometry higher-lie-theory higher-topos-theory history homological homological-algebra homotopy homotopy-theory homotopy-type-theory homtopy-type-theory infinity-groupoid integration-theory internal-categories kan lie lie-algebras lie-theory limit limits linear linear-algebra locale localization localization-theory logic manifolds mathematics measure measure-theory mechanics meta modal-logic model model-category-theory monoidal monoidal-category monoidal-category-theory morphism n-groups newpage noncommutative noncommutative-geometry object operator operator-algebra order-theory philosophy physics predicative pretopology pro-object probability-theory quantum quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry set set-theory sheaf simplicial site space stable-homotopy-theory stack string string-theory subobject supergeometry symplectic-geometry tannaka tensor terminology theory topologica-quantum-field-theory topology topos topos-theory torsor tqft type type-theory universal weighted-limit

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 23rd 2009
   • (edited Nov 23rd 2009)
   • PermaLink
   Author: Urs
   Format: MarkdownI added a section <a href="http://ncatlab.org/nlab/show/(infinity%2C1)-categorical+hom-space#enriched_homs_between_cofibrantfibrant_objects_6">Hom-spaces between cofibrant/fibrant objects</a> with a few lemmas and their proofs at [[(infinity,1)-categorical hom-space]]. (The proofs are intentionally very small-step and hopefully "pedagogical".) I also reworded the introduction part a bit and replied further in the old query box there. Effectively my point is: I am not overly happy with the title of that entry myself, but the alternatives proposed so far still strike me as worse. The main deficiency of the title is that it may sound a bit awkward. But it has the advantage of being fairly accuratively descriptive. But I won't be dogmatic about this. If there is a wide-spread desire to rename the entry, please feel free to do so.

   I added a section Hom-spaces between cofibrant/fibrant objects with a few lemmas and their proofs at

   (infinity,1)-categorical hom-space.

   (The proofs are intentionally very small-step and hopefully "pedagogical".)

   I also reworded the introduction part a bit and replied further in the old query box there.

   Effectively my point is: I am not overly happy with the title of that entry myself, but the alternatives proposed so far still strike me as worse. The main deficiency of the title is that it may sound a bit awkward. But it has the advantage of being fairly accuratively descriptive.

   But I won't be dogmatic about this. If there is a wide-spread desire to rename the entry, please feel free to do so.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 23rd 2009
   • PermaLink
   Author: Urs
   Format: MarkdownI also expanded the floating toc [[model category theory - contents]] by including: - a link to [[model structure on an over category]] in the examples section - a link to [[proper model category]] in the _refinements_ section - a section _presentation of (oo,1)-categories_ with four sub-links

   I also expanded the floating toc model category theory - contents by including:

   • a link to model structure on an over category in the examples section

   • a link to proper model category in the refinements section

   • a section presentation of (oo,1)-categories with four sub-links

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 23rd 2009
   • (edited Nov 23rd 2009)
   • PermaLink
   Author: Urs
   Format: Markdownreply to Toby in the query box at [[(infinity,1)-categorical hom-space]]. Maybe in the end the best is to choose whatever terminology but be sure that the punchline of the discussion we are having in that box is made an explicit _remark on terminology_ in the entry.

   reply to Toby in the query box at (infinity,1)-categorical hom-space.

   Maybe in the end the best is to choose whatever terminology but be sure that the punchline of the discussion we are having in that box is made an explicit remark on terminology in the entry.

4. • CommentRowNumber4.
   • CommentAuthorTobyBartels
   • CommentTimeNov 23rd 2009
   • PermaLink
   Author: TobyBartels
   Format: MarkdownIndeed.

   Indeed.

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMar 21st 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added to [[(infinity,1)-categorical hom-space]] a new sectin _[Hom-spaces of equivalences](http://ncatlab.org/nlab/show/%28infinity%2C1%29-categorical+hom-space#SpacesOfEquivalences)_ with a brief note on how the derived hom-space of equivalences in a model category is presented by the nerve of the subcategory of weak equivalences.

   I have added to (infinity,1)-categorical hom-space a new sectin Hom-spaces of equivalences with a brief note on how the derived hom-space of equivalences in a model category is presented by the nerve of the subcategory of weak equivalences.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeApr 16th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added to [[(infinity,1)-categorical hom-space]] a new section with a brief remark on its presentation by framings / simplicial Reedy resolutions (which for the moment just points to the coresponding section at [[simplicial model category]]). I have also slightly re-organized the sections such as to make it a tad more systematic. Eventually this entry deserves to be brushed up and prettified a bit more.

   I have added to (infinity,1)-categorical hom-space a new section with a brief remark on its presentation by framings / simplicial Reedy resolutions (which for the moment just points to the coresponding section at simplicial model category).

   I have also slightly re-organized the sections such as to make it a tad more systematic.

   Eventually this entry deserves to be brushed up and prettified a bit more.

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeApr 16th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexAdded some more details on "simplicial framings" in the section _[In terms of framings / simplicial Reedy resolutions](http://ncatlab.org/nlab/show/%28infinity%2C1%29-categorical+hom-space#Framings)_. There is some duplication now with the previous section. Need to find the time to edit the entry more.

   Added some more details on “simplicial framings” in the section In terms of framings / simplicial Reedy resolutions.

   There is some duplication now with the previous section. Need to find the time to edit the entry more.