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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.
   • CommentAuthornLab edit announcer
   • CommentTimeMay 17th 2021
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexstub article for regular infinity categories Anonymous <a href="https://ncatlab.org/nlab/revision/regular+%28infinity%2C1%29-category/1">v1</a>, <a href="https://ncatlab.org/nlab/show/regular+%28infinity%2C1%29-category">current</a>

   stub article for regular infinity categories

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 17th 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexThanks. I have just changed the "floating context menu" from "Higher category theory" to "$\infty$-Category theory". By the way, are you introducing the notion here, or should the page cite a reference? <a href="https://ncatlab.org/nlab/revision/diff/regular+%28infinity%2C1%29-category/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/regular+%28infinity%2C1%29-category/3">v3</a>, <a href="https://ncatlab.org/nlab/show/regular+%28infinity%2C1%29-category">current</a>

   Thanks. I have just changed the “floating context menu” from “Higher category theory” to “$\infty$-Category theory”.

   By the way, are you introducing the notion here, or should the page cite a reference?

   diff, v3, current

3. • CommentRowNumber3.
   • CommentAuthorHurkyl
   • CommentTimeMay 17th 2021
   • (edited May 17th 2021)
   • PermaLink
   Author: Hurkyl
   Format: MarkdownItexHuh. I would have thought you'd want to capture the notion of relation rather than the notion of epi-mono factorization. That is, I would have generalized the notion as a finitely complete category with the property that groupoids are effective, and that pullbacks preserve geometric realizations (or maybe just geometric realizations of groupoids). I actually thought about creating such a stub myself. Is there a relation between the two different ideas?

   Huh. I would have thought you’d want to capture the notion of relation rather than the notion of epi-mono factorization.

   That is, I would have generalized the notion as a finitely complete category with the property that groupoids are effective, and that pullbacks preserve geometric realizations (or maybe just geometric realizations of groupoids). I actually thought about creating such a stub myself.

   Is there a relation between the two different ideas?

4. • CommentRowNumber4.
   • CommentAuthorDavidRoberts
   • CommentTimeMay 17th 2021
   • PermaLink
   Author: DavidRoberts
   Format: MarkdownItexIt's not clear whether the $n$ in the definition is meant to vary over all $n\geq 0$, or if just one value of $n$ is needed.

   It’s not clear whether the $n$ in the definition is meant to vary over all $n\geq 0$, or if just one value of $n$ is needed.

5. • CommentRowNumber5.
   • CommentAuthorDmitri Pavlov
   • CommentTimeDec 14th 2023
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded an actual definition and a reference. The definition of an exact (∞,1)-category does not belong here, perhaps it should be moved to [[exact (∞,1)-category]]? <a href="https://ncatlab.org/nlab/revision/diff/regular+%28infinity%2C1%29-category/4">diff</a>, <a href="https://ncatlab.org/nlab/revision/regular+%28infinity%2C1%29-category/4">v4</a>, <a href="https://ncatlab.org/nlab/show/regular+%28infinity%2C1%29-category">current</a>

   Added an actual definition and a reference.

   The definition of an exact (∞,1)-category does not belong here, perhaps it should be moved to exact (∞,1)-category?

   diff, v4, current