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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.
   • CommentAuthornLab edit announcer
   • CommentTimeAug 24th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexPage created, but author did not leave any comments. Anonymous <a href="https://ncatlab.org/nlab/revision/equivalent-on-objects+functor/1">v1</a>, <a href="https://ncatlab.org/nlab/show/equivalent-on-objects+functor">current</a>

   Page created, but author did not leave any comments.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorMike Shulman
   • CommentTimeAug 29th 2022
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   Author: Mike Shulman
   Format: MarkdownItexIs this page really necessary?

   Is this page really necessary?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeAug 29th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexThis is one of half a dozen new entries that all consider notions of morphisms between categories with a fixed collection of objects. As I had suggested in discussion of another one of these ([here](https://nforum.ncatlab.org/discussion/15007/categories-with-the-same-collection-of-objects/?Focus=102255#Comment_102255)), the sensible thing to do would be to have one single page for **category with a fixed collection of objects** and then list these various notions of morphsism there. In fact, as I had also highlighted there, if we think of categories as (special cases of) stacks, then this is the notion of equipping a stack with an *atlas*, and that's a basic but important notion also outside of foundations, which would certainly deserve to have its own entry. (I could make these edits and re-arrangements, but not right now...)

   This is one of half a dozen new entries that all consider notions of morphisms between categories with a fixed collection of objects.

   As I had suggested in discussion of another one of these (here), the sensible thing to do would be to have one single page for category with a fixed collection of objects and then list these various notions of morphsism there.

   In fact, as I had also highlighted there, if we think of categories as (special cases of) stacks, then this is the notion of equipping a stack with an atlas, and that’s a basic but important notion also outside of foundations, which would certainly deserve to have its own entry.

   (I could make these edits and re-arrangements, but not right now…)