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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 definitions 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 k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum 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.
   • CommentAuthorUrs
   • CommentTimeJul 12th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexstarted adding to [[(infinity,1)-topos]] a section on the <a href="http://ncatlab.org/nlab/show/(infinity%2C1)-topos#ToposesCat">(oo,1)-category of (oo,1)-toposes</a>.

   started adding to (infinity,1)-topos a section on the (oo,1)-category of (oo,1)-toposes.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeOct 6th 2010
   • (edited Oct 6th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded to [[(infinity,1)-topos]] the article by Charles Rezk where he effectively (somewhat secretly) discusses the $\infty$-Giraud axioms of universal $\infty$-colimits in model theoretic terms. Also the followup by Wendt. (I am sure I referenced Rezk's article elsewhere already on the nLab. But not sure where! And it needs to be listed here in this entry.)

   added to (infinity,1)-topos the article by Charles Rezk where he effectively (somewhat secretly) discusses the $\infty$-Giraud axioms of universal $\infty$-colimits in model theoretic terms. Also the followup by Wendt.

   (I am sure I referenced Rezk’s article elsewhere already on the nLab. But not sure where! And it needs to be listed here in this entry.)

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeNov 23rd 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a section <a href="http://ncatlab.org/nlab/show/(infinity%2C1)-topos#ClosedMonoidalStructure">Closed monoidal structure</a> with statement and proof that every $(\infty,1)$-topos is a [[cartesian closed (infinity,1)-category]].

   added a section Closed monoidal structure with statement and proof that every $(\infty,1)$-topos is a cartesian closed (infinity,1)-category.

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeNov 23rd 2010
   • (edited Nov 23rd 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded in <a href="http://ncatlab.org/nlab/show/(infinity%2C1)-topos#ClosedMonoidalStructure">that section</a> statement and proof that the internal hom in an $infty$-topos respects finite colimits in the first argument: $$ [{\lim_\to}_i X_i, A] \simeq {\lim_\leftarrow}_i [X_i, A] \,. $$

   added in that section statement and proof that the internal hom in an $infty$-topos respects finite colimits in the first argument:

   $$[{\lim_\to}_i X_i, A] \simeq {\lim_\leftarrow}_i [X_i, A] \,.$$
5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeNov 24th 2010
   • (edited Nov 24th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added statement and proof (last one in <a href="http://ncatlab.org/nlab/show/(infinity%2C1)-topos#ClosedMonoidalStructure">this section</a>) that internal hom out of a constant $\infty$-stack produces the powering over $\infty$-groupoids $$ [LConst S, A] \simeq A^S $$

   I have added statement and proof (last one in this section) that internal hom out of a constant $\infty$-stack produces the powering over $\infty$-groupoids

   $$[LConst S, A] \simeq A^S$$
6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeNov 25th 2010
   • (edited Nov 25th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded to the Properties-section a subsection with a remark on <a href="http://ncatlab.org/nlab/show/(infinity%2C1)-topos#Powering">powering</a>.

   added to the Properties-section a subsection with a remark on powering.