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Abstract
We prove a class of equivalences of additive functor categories that are relevant to enumerative combinatorics, representation theory, and homotopy theory. Let X denote an additive category with finite direct sums and splitting idempotents. The class includes (a) the DoldPuppeKan theorem that simplicial objects in X are equivalent to chain complexes in X; (b) the observation of Church, Ellenberg and Farb [9] that Xvalued species are equivalent to Xvalued functors from the category of finite sets and injective partial functions; (c) a result T. Pirashvili calls of "DoldKan type" and so on. When X is semiabelian, we prove the adjunction that was an equivalence is now at least monadic, in the spirit of a theorem of D. Bourne.
Original language  English 

Pages (fromto)  43434367 
Number of pages  25 
Journal  Journal of Pure and Applied Algebra 
Volume  219 
Issue number  10 
DOIs  
Publication status  Published  Oct 2015 
Bibliographical note
A corrigendum exists for this article and can be found in Journal of Pure and Applied Algebra, 224(3), p.13641366, doi: 10.1016/j.jpaa.2019.07.002Fingerprint
Dive into the research topics of 'Combinatorial categorical equivalences of DoldKan type'. Together they form a unique fingerprint.Projects
 3 Finished

Monoidal categories and beyond: new contexts and new applications
Street, R., Verity, D., Lack, S., Garner, R. & MQRES Inter Tuition Fee only, M. I. T. F. O.
30/06/16 → 17/06/19
Project: Research

Structural homotopy theory: a categorytheoretic study
Street, R., Lack, S., Verity, D., Garner, R., MQRES, M., MQRES 3 (International), M. 3., MQRES 4 (International), M. & MQRES (International), M. (.
1/01/13 → 31/12/16
Project: Research
