scholarly journals A symmetric monoidal and equivariant Segal infinite loop space machine

2019 ◽  
Vol 223 (6) ◽  
pp. 2425-2454 ◽  
Author(s):  
Bertrand Guillou ◽  
J. Peter May ◽  
Mona Merling ◽  
Angélica M. Osorno
Keyword(s):  
Loop Space ◽  
Infinite Loop ◽  
Infinite Loop Space

scholarly journals SYMMETRIC MONOIDAL G-CATEGORIES AND THEIR STRICTIFICATION

2019 ◽  
Vol 71 (1) ◽  
pp. 207-246
Author(s):  
Bertrand J Guillou ◽  
J Peter May ◽  
Mona Merling ◽  
Angélica M Osorno
Keyword(s):  
Loop Space ◽  
General Category ◽  
Space Theory ◽  
Classifying Space ◽  
General Internal ◽  
Categorical Framework ◽  
Infinite Loop ◽  
Definition Of ◽  
A Finite Group ◽  
Infinite Loop Space

Abstract We give an operadic definition of a genuine symmetric monoidal $G$-category, and we prove that its classifying space is a genuine $E_\infty $$G$-space. We do this by developing some very general categorical coherence theory. We combine results of Corner and Gurski, Power and Lack to develop a strictification theory for pseudoalgebras over operads and monads. It specializes to strictify genuine symmetric monoidal $G$-categories to genuine permutative $G$-categories. All of our work takes place in a general internal categorical framework that has many quite different specializations. When $G$ is a finite group, the theory here combines with previous work to generalize equivariant infinite loop space theory from strict space level input to considerably more general category level input. It takes genuine symmetric monoidal $G$-categories as input to an equivariant infinite loop space machine that gives genuine $\Omega $-$G$-spectra as output.

scholarly journals Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory

2014 ◽  
Vol 7 (4) ◽  
pp. 1077-1117 ◽  
Author(s):  
Matthew Ando ◽  
Andrew J. Blumberg ◽  
David Gepner ◽  
Michael J. Hopkins ◽  
Charles Rezk
Keyword(s):  
Loop Space ◽  
Space Theory ◽  
Thom Spectra ◽  
Ring Spectra ◽  
Infinite Loop ◽  
Infinite Loop Space

scholarly journals Universality of multiplicative infinite loop space machines

2015 ◽  
Vol 15 (6) ◽  
pp. 3107-3153 ◽  
Author(s):  
David Gepner ◽  
Moritz Groth ◽  
Thomas Nikolaus
Keyword(s):  
Loop Space ◽  
Infinite Loop ◽  
Infinite Loop Space

The MultipleQ-Construction

1987 ◽  
Vol 39 (5) ◽  
pp. 1174-1209 ◽  
Author(s):  
J. F. Jardine
Keyword(s):  
Loop Space ◽  
Space Structure ◽  
Exact Category ◽  
Infinite Loop ◽  
Plus Construction ◽  
Infinite Loop Space

Products, and closely associated questions of infinite loop space structure, have always been a source of trouble in higher algebraicK-theory. From the first description of the product in terms of the plus construction, up to the current tendency to let the infinite loop space machines do it, the constructions have never been completely explicit, and many mistakes have resulted.Since Waldhausen introduced the doubleQ-construction [16], there has been the tantalizing prospect of an infinite loop space structure for the nerveof theQ-constructionof an exact category, which would be understandable to the man on the street, and which also would be well-behaved with respect to products induced by biexact pairings. Gillet [3] showed that most of these conditions could be met with his introduction of the multipleQ-construction. Shimakawa [14] filled in some of the details later.

scholarly journals Rings, modules, and algebras in infinite loop space theory

2006 ◽  
Vol 205 (1) ◽  
pp. 163-228 ◽  
Author(s):  
A.D. Elmendorf ◽  
M.A. Mandell
Keyword(s):  
Loop Space ◽  
Space Theory ◽  
Infinite Loop ◽  
Infinite Loop Space
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