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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.
   • CommentAuthornLab edit announcer
   • CommentTimeJan 7th 2023
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexstarting page on one-to-one correspondences Anonymous <a href="https://ncatlab.org/nlab/revision/one-to-one+correspondence/1">v1</a>, <a href="https://ncatlab.org/nlab/show/one-to-one+correspondence">current</a>

   starting page on one-to-one correspondences

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthornLab edit announcer
   • CommentTimeMay 17th 2024
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexthese are also called bitotal correspondences, as described by Mike Shulman in * [[Mike Shulman]], *Higher Observational Type Theory: An autonomous foundation for univalent mathematics* ([slides](https://home.sandiego.edu/~shulman/papers/chapman-fall2022.pdf)) Anonymouse <a href="https://ncatlab.org/nlab/revision/diff/one-to-one+correspondence/3">diff</a>, <a href="https://ncatlab.org/nlab/revision/one-to-one+correspondence/3">v3</a>, <a href="https://ncatlab.org/nlab/show/one-to-one+correspondence">current</a>

   these are also called bitotal correspondences, as described by Mike Shulman in

   • Mike Shulman, Higher Observational Type Theory: An autonomous foundation for univalent mathematics (slides)

   Anonymouse

   diff, v3, current

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeMay 17th 2024
   • PermaLink
   Author: Mike Shulman
   Format: MarkdownItexNo, a bitotal correspondence lacks uniqueness.

   No, a bitotal correspondence lacks uniqueness.