Higher Categories and Homotopical Algebra

Author(s):  
Denis-Charles Cisinski

Among the classes of invertebrate animals, the Bivalvia, with its extremely long fossil record and its preserved characters, which permit inferential anatomical reconstruction, comprises a group especially fit for phyletic analysis. Ideal for the investigation of the dynamics of speciation and the evolution of higher categories, bivalves represent a taxonomic unit whose systematics suffer from certain weaknesses. The relative narrowness of the anagenetic distances between lineages and the all-too-human tendency both to proliferate nomina and to elevate taxa partially obfuscate reality. The taxonomy of the Bivalvia is threatened by a cloying nomenclature both at specific and higher categorical levels. Reappraisal of various, recently proposed, systematic arrangements and judicious application of Occam’s Razor may allay the malaise of superfluity and promise the elaboration of a phyletically meaningful but somewhat simplified, utilitarian classification.



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


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






1975 ◽  
Vol 27 (4) ◽  
pp. 901-934 ◽  
Author(s):  
K. Varadarajan

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.



2017 ◽  
Vol 13 (4) ◽  
pp. 3261-3287
Author(s):  
Marco Benini ◽  
Kasia Rejzner ◽  
Alexander Schenkel ◽  
Christoph Schweigert


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