Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

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 21st 2018
   • (edited Jun 21st 2018)
   • PermaLink
   Author: Urs
   Format: MarkdownItexwhat used to be under "Examples" was rather two illustrations of what the definition means. So I moved that to after the definition, and instead included under _[Examples](https://ncatlab.org/nlab/show/preserved+limit#Examples)_ the following pointers to classes of examples: * [[limits preserve limits]] * [[adjoints preserve (co-)limits]] * [[hom-functor preserves limits]] <a href="https://ncatlab.org/nlab/revision/diff/preserved+limit/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/preserved+limit/10">v10</a>, <a href="https://ncatlab.org/nlab/show/preserved+limit">current</a>

   what used to be under “Examples” was rather two illustrations of what the definition means. So I moved that to after the definition, and instead included under Examples the following pointers to classes of examples:

   • limits preserve limits

   • adjoints preserve (co-)limits

   • hom-functor preserves limits

   diff, v10, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 11th 2022
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded some references: * [[Francis Borceux]], §2.4 in: *[[Handbook of Categorical Algebra]]* Vol. 1: *Basic Category Theory* &lbrack;[doi:10.1017/CBO9780511525858](https://doi.org/10.1017/CBO9780511525858)&rbrack; * [[Emily Riehl]], §3.3 in: *[[Category Theory in Context]]*, Dover Publications (2017) &lbrack;[pdf](http://www.math.jhu.edu/~eriehl/context.pdf), [book website](http://www.math.jhu.edu/~eriehl/context/)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/preserved+limit/12">diff</a>, <a href="https://ncatlab.org/nlab/revision/preserved+limit/12">v12</a>, <a href="https://ncatlab.org/nlab/show/preserved+limit">current</a>

   added some references:

   • Francis Borceux, §2.4 in: Handbook of Categorical Algebra Vol. 1: Basic Category Theory [doi:10.1017/CBO9780511525858]

   • Emily Riehl, §3.3 in: Category Theory in Context, Dover Publications (2017) [pdf, book website]

   diff, v12, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 20th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Saunders MacLane]], §V.4 of: *[[Categories for the Working Mathematician]]*, Graduate Texts in Mathematics **5** Springer (1971, second ed. 1997) &lbrack;[doi:10.1007/978-1-4757-4721-8](https://link.springer.com/book/10.1007/978-1-4757-4721-8)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/preserved+limit/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/preserved+limit/15">v15</a>, <a href="https://ncatlab.org/nlab/show/preserved+limit">current</a>

   added pointer to:

   • Saunders MacLane, §V.4 of: Categories for the Working Mathematician, Graduate Texts in Mathematics 5 Springer (1971, second ed. 1997) [doi:10.1007/978-1-4757-4721-8]

   diff, v15, current

4. • CommentRowNumber4.
   • CommentAuthorJohn Baez
   • CommentTimeMay 10th 2024
   • PermaLink
   Author: John Baez
   Format: MarkdownItexAdded example: the Yoneda embedding preserves limits. If we ever include a proof of that, we can link to that. <a href="https://ncatlab.org/nlab/revision/diff/preserved+limit/17">diff</a>, <a href="https://ncatlab.org/nlab/revision/preserved+limit/17">v17</a>, <a href="https://ncatlab.org/nlab/show/preserved+limit">current</a>

   Added example: the Yoneda embedding preserves limits. If we ever include a proof of that, we can link to that.

   diff, v17, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMay 10th 2024
   • (edited May 10th 2024)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded ([here](https://ncatlab.org/nlab/show/preserved+limit#ExampleYonedaEmbedding)) pointer to the proof <a href="https://ncatlab.org/nlab/revision/diff/preserved+limit/18">diff</a>, <a href="https://ncatlab.org/nlab/revision/preserved+limit/18">v18</a>, <a href="https://ncatlab.org/nlab/show/preserved+limit">current</a>

   added (here) pointer to the proof

   diff, v18, current