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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.
   • CommentAuthorUrs
   • CommentTimeMar 5th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexI am finally creating this entry --- meant as a bare list of hyperlinked terms to be `!include`-ed into the "Related concepts"-sections of the respective entries --- for ease of synchronizing this list across all these entries. (I am not sold on the title "mathematical statements", it's just the best I could come up with after a minute of thinking about it). I am creating this now with the following list, but this may change as I now go through all the related entries: *** * [[language]], [[theory]] * [[judgement]], [[assertion]] * [[hypothesis]], [[consequence]] * [[axiom]] * [[definition]] * [[inductive definition]] * [[coinductive definition]] * [[lemma]] * [[proposition]]/[[type]] ([[propositions as types]]) * [[theorem]] * [[proof]]/[[program]] ([[proofs as programs]]) * [[example]] * [[counterexample]] * [[folklore]] * [[conjecture]] * [[analogy]] * [[paradox]] * [[exercise]] *** <a href="https://ncatlab.org/nlab/revision/mathematical+statements+---+contents/1">v1</a>, <a href="https://ncatlab.org/nlab/show/mathematical+statements+---+contents">current</a>

   I am finally creating this entry — meant as a bare list of hyperlinked terms to be !include-ed into the “Related concepts”-sections of the respective entries — for ease of synchronizing this list across all these entries.

   (I am not sold on the title “mathematical statements”, it’s just the best I could come up with after a minute of thinking about it).

   I am creating this now with the following list, but this may change as I now go through all the related entries:

   ---

   • language, theory

   • judgement, assertion

   • hypothesis, consequence

   • axiom

   • definition

     • inductive definition

     • coinductive definition

   • lemma

   • proposition/type (propositions as types)

   • theorem

   • proof/program (proofs as programs)

   • example

   • counterexample

   • folklore

   • conjecture

   • analogy

   • paradox

   • exercise

   ---

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 26th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded the item *[[tautology]]* <a href="https://ncatlab.org/nlab/revision/diff/mathematical+statements+---+contents/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/mathematical+statements+---+contents/2">v2</a>, <a href="https://ncatlab.org/nlab/show/mathematical+statements+---+contents">current</a>

   added the item tautology

   diff, v2, current