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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.
   • CommentAuthorUrs
   • CommentTimeJun 13th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexThis entry is currently undecided as to whether "full subcategory" inclusion requires the functor to be an injection on objects. It begins by pointing to _[[subcategory]]_ which does require this, but before long it speaks about fully faitful functors being full subcategory inclusions. This will be confusing to newcomers. There should be at least some comments about invariance under equivalence of categories. Ah, now I see that at _[[subcategory]]_ there is such a discussion ([here](https://ncatlab.org/nlab/show/subcategory#VariantsInAccordWithThePrincipleOfEquivalence)). Hm, there is some room for cleaning-up here. <a href="https://ncatlab.org/nlab/revision/diff/full+subcategory/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/full+subcategory/10">v10</a>, <a href="https://ncatlab.org/nlab/show/full+subcategory">current</a>

   This entry is currently undecided as to whether “full subcategory” inclusion requires the functor to be an injection on objects. It begins by pointing to subcategory which does require this, but before long it speaks about fully faitful functors being full subcategory inclusions.

   This will be confusing to newcomers. There should be at least some comments about invariance under equivalence of categories.

   Ah, now I see that at subcategory there is such a discussion (here). Hm, there is some room for cleaning-up here.

   diff, v10, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeJun 13th 2018
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have added an Idea-section that clarifies the subtlety, and I divided the Definition-section into "Non-invariant definition" and "Invariant definition". <a href="https://ncatlab.org/nlab/revision/diff/full+subcategory/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/full+subcategory/10">v10</a>, <a href="https://ncatlab.org/nlab/show/full+subcategory">current</a>

   I have added an Idea-section that clarifies the subtlety, and I divided the Definition-section into “Non-invariant definition” and “Invariant definition”.

   diff, v10, current