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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 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 nforum 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.
   • CommentAuthorTim_Porter
   • CommentTimeJan 24th 2014
   • (edited Jan 25th 2014)
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   Author: Tim_Porter
   Format: MarkdownItexSo as to get rid of a grey unattached link, I created a stub for [[finitely presented group ]].

   So as to get rid of a grey unattached link, I created a stub for finitely presented group.

2. • CommentRowNumber2.
   • CommentAuthorTodd_Trimble
   • CommentTimeJan 24th 2014
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   Author: Todd_Trimble
   Format: MarkdownItexIt's certainly the definition that one will find in the literature, but I wonder if I'm alone in finding the grammar a little odd here. According to this definition, there is no difference in meaning between a "finitely presented group" and a "finitely presentable group". But if it were up to me, I would refer to a finitely presented group only if I had a specific finite presentation in mind (a particular diagram exhibiting $G$ as a coequalizer of a pair of morphisms between finitely generated free groups).

   It’s certainly the definition that one will find in the literature, but I wonder if I’m alone in finding the grammar a little odd here. According to this definition, there is no difference in meaning between a “finitely presented group” and a “finitely presentable group”. But if it were up to me, I would refer to a finitely presented group only if I had a specific finite presentation in mind (a particular diagram exhibiting $G$ as a coequalizer of a pair of morphisms between finitely generated free groups).

3. • CommentRowNumber3.
   • CommentAuthorMike Shulman
   • CommentTimeJan 24th 2014
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   Author: Mike Shulman
   Format: MarkdownItexI agree with Todd. On the other hand, that's what we get if we interpret "there is" in the propositions-as-types manner as a $\Sigma$... (-:

   I agree with Todd. On the other hand, that’s what we get if we interpret “there is” in the propositions-as-types manner as a $\Sigma$… (-:

4. • CommentRowNumber4.
   • CommentAuthorTim_Porter
   • CommentTimeJan 24th 2014
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   Author: Tim_Porter
   Format: MarkdownItexIn fact you both mirror the thought that came to me when I typed it out! I would also like to ask whether you feel that the isomorphism from the quotient group to $G$ should be part of the definition of a presentation. My preference is that it should be but that then it can be set aside.

   In fact you both mirror the thought that came to me when I typed it out! I would also like to ask whether you feel that the isomorphism from the quotient group to $G$ should be part of the definition of a presentation. My preference is that it should be but that then it can be set aside.

5. • CommentRowNumber5.
   • CommentAuthorTim_Porter
   • CommentTimeJan 24th 2014
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   Author: Tim_Porter
   Format: MarkdownItexI have made a change to the entry. Try the new one for size!

   I have made a change to the entry. Try the new one for size!

6. • CommentRowNumber6.
   • CommentAuthorMike Shulman
   • CommentTimeJan 27th 2014
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   Author: Mike Shulman
   Format: MarkdownItexRe #4, of course it should be! I would tend to phrase it as "a presentation of $G$ is a coequalizer diagram $F R \rightrightarrows F X \twoheadrightarrow G$".

   Re #4, of course it should be! I would tend to phrase it as “a presentation of $G$ is a coequalizer diagram $F R \rightrightarrows F X \twoheadrightarrow G$”.

7. • CommentRowNumber7.
   • CommentAuthorTim_Porter
   • CommentTimeJan 27th 2014
   • (edited Jan 27th 2014)
   • PermaLink
   Author: Tim_Porter
   Format: MarkdownItexThat sounds about right. As Ronnie and Johannes Huebschmann found in their paper on identities among relations, you need that to make sense of the identities. I have edited the entry accordingly.

   That sounds about right. As Ronnie and Johannes Huebschmann found in their paper on identities among relations, you need that to make sense of the identities.

   I have edited the entry accordingly.