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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 finite 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 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.
   • CommentAuthorDmitri Pavlov
   • CommentTimeDec 13th 2023
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexCreated: \tableofcontents ## Idea […] ## Related concepts * [[canonical model structure]] ## References * [[Tomas Everaert]], [[Rudger W. Kieboom]], [[Tim van der Linden]], _Model structures for homotopy of internal categories_, Theory and Applications of Categories 15:3 (2005) 66-94. [tac:15-03](http://www.tac.mta.ca/tac/volumes/15/3/15-03abs.html), [EuDML:125875](https://eudml.org/doc/125875). * [[Goeffroy Horel]], _A model structure on internal categories in simplicial sets_, Theory and Applications of Categories 30:20 (2015), 704-750. [arXiv](https://arxiv.org/abs/1403.6873), [TAC](http://www.tac.mta.ca/tac/volumes/30/20/30-20abs.html). <a href="https://ncatlab.org/nlab/revision/model+structure+on+internal+categories/1">v1</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+internal+categories">current</a>

   Created:

   \tableofcontents

   Idea

   […]

   Related concepts

   • canonical model structure

   References

   • Tomas Everaert, Rudger W. Kieboom, Tim van der Linden, Model structures for homotopy of internal categories, Theory and Applications of Categories 15:3 (2005) 66-94. tac:15-03, EuDML:125875.

   • Goeffroy Horel, A model structure on internal categories in simplicial sets, Theory and Applications of Categories 30:20 (2015), 704-750. arXiv, TAC.

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeDec 13th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe original discussion of the [[canonical model structure on Cat]] is already in the generality of internal categories in topoi ([Joyal & Tierney 1991](https://ncatlab.org/nlab/show/canonical+model+structure+on+Cat#JoyalTierney91)).

   The original discussion of the canonical model structure on Cat is already in the generality of internal categories in topoi (Joyal & Tierney 1991).

3. • CommentRowNumber3.
   • CommentAuthorDmitri Pavlov
   • CommentTimeDec 13th 2023
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexAdded: [[internal category|Categories internal to]] [[toposes]]: * {#JoyalTierney91} [[André Joyal]], [[Myles Tierney]], Thm. 4 (p. 232) of: *Strong stacks and classifying spaces*, in: *Category Theory* Lecture Notes in Mathematics **1488**, Springer (1991) 213-236 &lbrack;[doi:10.1007/BFb0084222](https://doi.org/10.1007/BFb0084222)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/model+structure+on+internal+categories/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/model+structure+on+internal+categories/2">v2</a>, <a href="https://ncatlab.org/nlab/show/model+structure+on+internal+categories">current</a>

   Added:

   Categories internal to toposes:

   • {#JoyalTierney91} André Joyal, Myles Tierney, Thm. 4 (p. 232) of: Strong stacks and classifying spaces, in: Category Theory Lecture Notes in Mathematics 1488, Springer (1991) 213-236 [doi:10.1007/BFb0084222]

   diff, v2, current