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Higher-dimensional algebra
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21	The intuitions of higher dimensional algebra for the study of structured space∗ Ronald Brown and Timothy Porter School of Computer Science Bangor University Gwynedd LL57 1UT, UK Add to Reading List Source URL: pages.bangor.ac.uk Language: English - Date: 2009-01-20 10:10:07 Homotopy theory Category theory Algebraic topology Higher category theory Algebraic structures Groupoid Seifert–van Kampen theorem Higher-dimensional algebra Homotopy group Abstract algebra Mathematics Algebra
22	Crossed complexes and higher homotopy groupoids as non commutative tools for higher dimensional local-to-global problems∗ Ronald Brown† March 1, 2009 Add to Reading List Source URL: pages.bangor.ac.uk Language: English - Date: 2009-03-01 12:04:52 Homotopy theory Algebraic topology Category theory Higher category theory Algebraic structures Double groupoid Crossed module Groupoid Seifert–van Kampen theorem Abstract algebra Topology Mathematics
23	Traces in low-dimensional algebra Simon Willerton University of Sheffield Tr& (f ) := Tr (f ) := Add to Reading List Source URL: www.simonwillerton.staff.shef.ac.uk Language: English - Date: 2013-09-03 07:35:50 Algebra 2-category Functor Natural transformation Bimodule Category Product Enriched category Fibred category Category theory Abstract algebra Higher category theory
24	Groups, groupoids and higher groupoids in algebraic topology An area of mathematics in which nonabelian structures have proved important is algebraic topology, where the fundamental group π1 (X, a) of a space X at a bas Add to Reading List Source URL: pages.bangor.ac.uk Language: English - Date: 2010-12-20 11:50:11 Homotopy theory Category theory Higher category theory Algebraic topology Algebraic structures Double groupoid Seifert–van Kampen theorem Higher-dimensional algebra Homotopy group Abstract algebra Topology Mathematics
25	Some Context for Higher Dimensional Group Theory Brandt’s Gauss’ Add to Reading List Source URL: pages.bangor.ac.uk Language: English - Date: 2004-04-13 12:22:35 Homotopy theory Algebraic structures Mathematics Algebra Groupoid Languages of Germany Latin alphabets Abstract algebra Category theory
26	Homotopy theory begins with the homotopy groups πn (X) , which are the natural higher-dimensional analogs of the fundamental group. These higher homotopy groups have certain formal similarities with homology groups. For example, πn (X) turns out to be always abelian for n ≥ 2 , and there are relative homotopy groups fitting into a long exact sequence just like the long exact sequence of homology groups. Add to Reading List Source URL: www.math.cornell.edu Language: English - Date: 2013-06-04 09:21:10 Algebraic topology Homotopy group Homotopy Fundamental group Eilenberg–MacLane space CW complex H-space Contractible space Path Topology Homotopy theory Abstract algebra
27	[removed]–22] Ver[removed] Add to Reading List Source URL: www.ritsumei.ac.jp Language: English - Date: 2004-04-13 01:57:26 Monoidal categories Group theory Homotopy theory John C. Baez N-group Higher-dimensional algebra Monoid Bicategory PRO Category theory Abstract algebra Higher category theory
28	Foundations and Applications of Higher-Dimensional Directed Type Theory Robert Harper and Daniel R. Licata Add to Reading List Source URL: www.cs.cmu.edu Language: English - Date: 2011-05-26 15:05:42 Type theory Logic in computer science Algebraic topology Dependently typed programming Proof theory Curry–Howard correspondence Category theory Equivalence of categories Sheaf Mathematics Abstract algebra Mathematical logic
29	Theory and Applications of Categories, Vol. 24, No. 18, 2010, pp. 489–553. HIGHER DIMENSIONAL ALGEBRA VII: GROUPOIDIFICATION Add to Reading List Source URL: www.tac.mta.ca Language: English - Date: 2010-11-12 15:17:58 Category theory Algebraic structures Homotopy theory Symmetry Group theory Groupoid Lie groupoid Group action Higher-dimensional algebra Abstract algebra Algebra Mathematics
30	Higher-Dimensional Categories: an illustrated guide book Add to Reading List Source URL: cheng.staff.shef.ac.uk Language: English - Date: 2006-10-26 07:27:22 Abstract algebra Algebraic topology Operad theory Simplicial set Definition Nerve Intuition Adjoint functors E∞-operad Category theory Mathematics Algebra

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