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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 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.
   • CommentAuthorUrs
   • CommentTimeOct 1st 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Charles Rezk]], *Generalizing accessible ∞-categories*, 2021 ([pdf](https://faculty.math.illinois.edu/~rezk/accessible-cat-thoughts.pdf)). <a href="https://ncatlab.org/nlab/revision/diff/accessible+%28infinity%2C1%29-category/25">diff</a>, <a href="https://ncatlab.org/nlab/revision/accessible+%28infinity%2C1%29-category/25">v25</a>, <a href="https://ncatlab.org/nlab/show/accessible+%28infinity%2C1%29-category">current</a>

   added pointer to:

   • Charles Rezk, Generalizing accessible ∞-categories, 2021 (pdf).

   diff, v25, current

2. • CommentRowNumber2.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 1st 2021
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexAny opportunities for HoTT-ists to help Charles out there?

   Any opportunities for HoTT-ists to help Charles out there?

3. • CommentRowNumber3.
   • CommentAuthorDavid_Corfield
   • CommentTimeOct 1st 2021
   • PermaLink
   Author: David_Corfield
   Format: MarkdownItexI see he refers to * Marie Bjerrum, Peter Johnstone, Tom Leinster, and William F. Sawin, Notes on commutation of limits and colimits, Theory Appl. Categ. 30 (2015), Paper No. 15, 527–532. which from this [discussion](https://golem.ph.utexas.edu/category/2013/12/commuting_limits_and_colimits.html) looked like a homotopical (and presumably HoTT) setting was simpler.

   I see he refers to

   • Marie Bjerrum, Peter Johnstone, Tom Leinster, and William F. Sawin, Notes on commutation of limits and colimits, Theory Appl. Categ. 30 (2015), Paper No. 15, 527–532.

   which from this discussion looked like a homotopical (and presumably HoTT) setting was simpler.