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Homotopy linear algebra

Author
Galvez, M.; Kock, J.; Tonks, A.
Type of activity
Journal article
Journal
Proceedings of the Royal Society of Edinburgh: Section A Mathematics
Date of publication
2018-04
Volume
148
Number
2
First page
293
Last page
325
DOI
https://doi.org/10.1017/S0308210517000208 Open in new window
Repository
http://hdl.handle.net/2117/112830 Open in new window
URL
https://www.cambridge.org/core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics/article/homotopy-linear-algebra/8E584127A7FB28AE5520B6604C7FC3C2 Open in new window
Abstract
By homotopy linear algebra we mean the study of linear functors between slices of the 8-category of 8-groupoids, subject to certain finiteness conditions. After some standard definitions and results, we assemble said slices into 8-categories to model the duality between vector spaces and profinite-dimensional vector spaces, and set up a global notion of homotopy cardinality à la Baez, Hoffnung and Walker compatible with this duality. We needed these results to support our work on incidence alge...
Citation
Galvez, M., Kock, J., Tonks, A. Homotopy linear algebra. "Proceedings of the Royal Society of Edinburgh: Section A Mathematics", Abril 2018, Volume 148, Issue 2, p. 293-325
Keywords
duality, homotopy cardinality, homotopy finiteness, infinity-groupoids, linear algebra
Group of research
GEOMVAP - Geometry of Manifolds and Applications

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