Pairings in infinite loop space theory

1977 ◽  
pp. 244-256
Author(s):  
J. Peter May
Keyword(s):  
Loop Space ◽  
Space Theory ◽  
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 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

scholarly journals The spectra associated to ℐ-monoids

1978 ◽  
Vol 84 (2) ◽  
pp. 313-322 ◽  
Author(s):  
J. P. May
Keyword(s):  
Loop Space ◽  
Geometric Topology ◽  
Space Theory ◽  
Classifying Spaces ◽  
Infinite Loop ◽  
Infinite Loop Space

In this final sequel to (9), I shall prove a general consistency statement which seems to me to complete the foundations of infinite loop space theory. In particular, this result will specialize to yield the last step of the proof of the following theorem about the stable classifying spaces of geometric topology.

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
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