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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.
   • CommentAuthorUrs
   • CommentTimeMay 23rd 2020
   • (edited May 23rd 2020)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have completed publication data (and missing words in title) for the single reference: * [[Jean-Louis Loday]], [[Teimuraz Pirashvili]], _The tensor category of linear maps and Leibniz algebras_, Georg. Math. J. vol. 5, n.3 (1998) 263--276 ([doi:10.1023/B:GEOR.0000008125.26487.f3](https://link.springer.com/article/10.1023/B:GEOR.0000008125.26487.f3)) <a href="https://ncatlab.org/nlab/revision/diff/Loday-Pirashvili+category/10">diff</a>, <a href="https://ncatlab.org/nlab/revision/Loday-Pirashvili+category/10">v10</a>, <a href="https://ncatlab.org/nlab/show/Loday-Pirashvili+category">current</a>

   I have completed publication data (and missing words in title) for the single reference:

   • Jean-Louis Loday, Teimuraz Pirashvili, The tensor category of linear maps and Leibniz algebras, Georg. Math. J. vol. 5, n.3 (1998) 263–276 (doi:10.1023/B:GEOR.0000008125.26487.f3)

   diff, v10, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 23rd 2020
   • PermaLink
   Author: Urs
   Format: MarkdownItexThe following query box was still sitting in the entry. I am hereby moving it from there to here: *** +-- {: .query} [[Tim Porter|Tim]]: Methinks that we need some comment on the evident connection with [[Baez–Crans 2-vector space]]. I think I remember seeing some paper on 2-vector spaces that mentions the connection. Whether or not it exploited that connection has slipped my memory. Can Zoran say something on this? [[Zoran Škoda|Zoran]] Surely in char 0, internal categories to vector spaces are the same as 2-term chain complexes, but if one translates strict associative algebra, Lie algebra etc. internal to the categories of internal categories in $Vec_k$ then one has more on the internal category side then on LP side because of the truncation of the tensor product. So every strict Lie algebra in Baez-Crans 2-vector spaces gives an examples of an internal Lie algebra in LP but not other way around. Eventually I will put some treatment of this, but it is not that simple to write it clearly, so it will wait a bit for now. =--

   The following query box was still sitting in the entry. I am hereby moving it from there to here:

   ---

   +– {: .query}

   Tim: Methinks that we need some comment on the evident connection with Baez–Crans 2-vector space. I think I remember seeing some paper on 2-vector spaces that mentions the connection. Whether or not it exploited that connection has slipped my memory. Can Zoran say something on this?

   Zoran Surely in char 0, internal categories to vector spaces are the same as 2-term chain complexes, but if one translates strict associative algebra, Lie algebra etc. internal to the categories of internal categories in $Vec_k$ then one has more on the internal category side then on LP side because of the truncation of the tensor product. So every strict Lie algebra in Baez-Crans 2-vector spaces gives an examples of an internal Lie algebra in LP but not other way around. Eventually I will put some treatment of this, but it is not that simple to write it clearly, so it will wait a bit for now.

   =–