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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 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 sheaves 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
   • CommentTimeNov 5th 2010
   • PermaLink
   Author: Urs
   Format: MarkdownItexI worked a bit on bringing the list of structures present in a cohesive (oo,1)-topos into shape, expanding it and filling in details. See the table of contents at [[cohesive (infinity,1)-topos]].

   I worked a bit on bringing the list of structures present in a cohesive (oo,1)-topos into shape, expanding it and filling in details. See the table of contents at cohesive (infinity,1)-topos.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeNov 6th 2010
   • (edited Nov 6th 2010)
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave posted on the Caf&eacute; about this: <a href="http://golem.ph.utexas.edu/category/2010/11/structures_in_a_cohesive_topos.html">here</a>

   have posted on the Café about this: here

3. • CommentRowNumber3.
   • CommentAuthorColin Tan
   • CommentTimeJul 17th 2014
   • PermaLink
   Author: Colin Tan
   Format: TextIs a oo-groupoid codiscrete if and only if its corresponding effective epimorphism has target the terminal object?

   Is a oo-groupoid codiscrete if and only if its corresponding effective epimorphism has target the terminal object?
4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJul 17th 2014
   • (edited Jul 17th 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexProbably this question originates in a clash of terminology: there is the concept of [[codiscrete groupoid]] and there is the concept of [[codiscrete object]] in [[cohesion]]. Applied to cohesive groupoid objects, these concepts are orthogonal to each other: the first refers to homotopy-theoretic codiscreneteness, the second to geometric codiscreteness. If you think of the first variant, then the answer to your question is "yes", by definition. If however you think of the second variant then the question does not really apply, or if one takes it literally then the answer is "no".

   Probably this question originates in a clash of terminology: there is the concept of codiscrete groupoid and there is the concept of codiscrete object in cohesion. Applied to cohesive groupoid objects, these concepts are orthogonal to each other: the first refers to homotopy-theoretic codiscreneteness, the second to geometric codiscreteness.

   If you think of the first variant, then the answer to your question is “yes”, by definition. If however you think of the second variant then the question does not really apply, or if one takes it literally then the answer is “no”.