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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
   • CommentTimeMay 11th 2022
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexPage created, but author did not leave any comments. Anonymous <a href="https://ncatlab.org/nlab/revision/subtype/1">v1</a>, <a href="https://ncatlab.org/nlab/show/subtype">current</a>

   Page created, but author did not leave any comments.

   Anonymous

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 2nd 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have prefixed the Idea-section ([here](https://ncatlab.org/nlab/show/subtype#Idea)) with a quick general idea of subtypes invoking $Prop$-types and added a bunch of references ([here](https://ncatlab.org/nlab/show/subtype#References)) <a href="https://ncatlab.org/nlab/revision/diff/subtype/13">diff</a>, <a href="https://ncatlab.org/nlab/revision/subtype/13">v13</a>, <a href="https://ncatlab.org/nlab/show/subtype">current</a>

   I have prefixed the Idea-section (here) with a quick general idea of subtypes invoking $Prop$-types

   and added a bunch of references (here)

   diff, v13, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeAug 13th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Martin Hofmann]], [[Benjamin Pierce]], *Positive Subtyping*, Information and Computation **126** 1 (1996) 11-33 &lbrack;[doi:10.1006/inco.1996.0031](https://doi.org/10.1006/inco.1996.0031)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/subtype/15">diff</a>, <a href="https://ncatlab.org/nlab/revision/subtype/15">v15</a>, <a href="https://ncatlab.org/nlab/show/subtype">current</a>

   added pointer to:

   • Martin Hofmann, Benjamin Pierce, Positive Subtyping, Information and Computation 126 1 (1996) 11-33 [doi:10.1006/inco.1996.0031]

   diff, v15, current

4. • CommentRowNumber4.
   • CommentAuthornLab edit announcer
   • CommentTimeSep 15th 2023
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexsubtypes in type theory are talked about in section 1.1 of the following reference: * [[Felix Cherubini]], [[Thierry Coquand]], [[Matthias Hutzler]], *A Foundation for Synthetic Algebraic Geometry* ([pdf](https://felix-cherubini.de/iag.pdf)) type theorist <a href="https://ncatlab.org/nlab/revision/diff/subtype/16">diff</a>, <a href="https://ncatlab.org/nlab/revision/subtype/16">v16</a>, <a href="https://ncatlab.org/nlab/show/subtype">current</a>

   subtypes in type theory are talked about in section 1.1 of the following reference:

   • Felix Cherubini, Thierry Coquand, Matthias Hutzler, A Foundation for Synthetic Algebraic Geometry (pdf)

   type theorist

   diff, v16, current

5. • CommentRowNumber5.
   • CommentAuthorRodMcGuire
   • CommentTimeSep 15th 2023
   • PermaLink
   Author: RodMcGuire
   Format: MarkdownItexthat should be * [[Felix Cherubini]], [[Thierry Coquand]], [[Matthias Hutzler]], *A Foundation for Synthetic Algebraic Geometry* (2023) &lbrack;[arXiv:2307.00073](https://arxiv.org/abs/2307.00073)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/subtype/17">diff</a>, <a href="https://ncatlab.org/nlab/revision/subtype/17">v17</a>, <a href="https://ncatlab.org/nlab/show/subtype">current</a>

   that should be

   • Felix Cherubini, Thierry Coquand, Matthias Hutzler, A Foundation for Synthetic Algebraic Geometry (2023) [arXiv:2307.00073]

   diff, v17, current