Cubical homotopical algebra and cochain algebras

1996 ◽  
Vol 170 (1) ◽  
pp. 147-186 ◽  
Author(s):  
Marco Grandis
Keyword(s):  
Homotopical Algebra

scholarly journals A homotopical algebra of graphs related to zeta series

2009 ◽  
Vol 11 (1) ◽  
pp. 171-184
Author(s):  
Terrence Bisson ◽  
Aristide Tsemo
Keyword(s):  
Homotopical Algebra

Numerical Invariants in Homotopical Algebra, I

1975 ◽  
Vol 27 (4) ◽  
pp. 901-934 ◽  
Author(s):  
K. Varadarajan
Keyword(s):  
Homotopy Theory ◽  
Algebra I ◽  
Homotopical Algebra ◽  
Numerical Invariants ◽  
Set Up ◽  
Lusternik Schnirelmann ◽  
Classical Homotopy

Classically CW-complexes were found to be the best suited objects for studying problems in homotopy theory. Certain numerical invariants associated to a CW-complex X such as the Lusternik-Schnirelmann Category of X, the index of nilpotency of ᘯ(X), the cocategory of X, the index of conilpotency of ∑ (X) have been studied by Eckmann, Hilton, Berstein and Ganea, etc. Recently D. G. Quillen [6] has developed homotopy theory for categories satisfying certain axioms. In the axiomatic set up of Quillen the duality observed in classical homotopy theory becomes a self-evident phenomenon, the axioms being so formulated.

Mini-Workshop: New Interactions between Homotopical Algebra and Quantum Field Theory

2017 ◽  
Vol 13 (4) ◽  
pp. 3261-3287
Author(s):  
Marco Benini ◽  
Kasia Rejzner ◽  
Alexander Schenkel ◽  
Christoph Schweigert
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Quantum Field ◽  
Homotopical Algebra ◽  
New Interactions

Homotopical Algebra

1967 ◽  
Author(s):  
Daniel G. Quillen
Keyword(s):  
Homotopical Algebra

Homotopical algebra and triangulated categories

1995 ◽  
Vol 118 (2) ◽  
pp. 259-285 ◽  
Author(s):  
Marco Grandis
Keyword(s):  
Triangulated Category ◽  
Triangulated Categories ◽  
Homotopical Algebra ◽  
Abstract Setting

AbstractWe study here the connections between the well known Puppe-Verdier notion of triangulated category and an abstract setting for homotopical algebra, based on homotopy kernels and cokernels, which was expounded by the author in [11, 13[.We show that a right-homotopical category A (having well-behaved homotopy cokernels, i.e. mapping cones) has a sort of weak triangulated structure with regard to the suspension endofunctor σ, called σ-homotopical category. If A is homotopical and h-stable (in a sense related to the suspension-loop adjunction), this structure is also h-stable, i.e. satisfies ‘up to homotopy’ the axioms of Verdier[29[ for a triangulated category, excepting the octahedral one which depends on some further elementary conditions on the cone endofunctor of A. Every σ-homotopical category can be stabilized, by two universal procedures, respectively initial and terminal.

scholarly journals Homotopical algebra for C*-algebras

2013 ◽  
Vol 7 (4) ◽  
pp. 981-1006 ◽  
Author(s):  
Otgonbayar Uuye
Keyword(s):  
Homotopical Algebra ◽  
C Algebras
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