5 citations · 12 across the 22 of their papers we have counts for
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On the James and Hilton-Milnor Splittings, & the metastable EHP sequence
Sanath K. Devalapurkar, Peter J. Haine
This note provides modern proofs of some classical results in algebraic topology, such as the James Splitting, the Hilton-Milnor Splitting, and the metastable EHP sequence. We prov…
Pyknotic objects, I. Basic notions
Clark Barwick, Peter Haine
Pyknotic objects are (hyper)sheaves on the site of compacta. These provide a convenient way to do algebra and homotopy theory with additional topological information present. This…
On coherent topoi & coherent -localic -topoi
Peter J. Haine
In this note we prove the following useful fact that seems to be missing from the literature: the -category of coherent ordinary topoi (in the sense of SGA4) is equivalent…
Exodromy for stacks
Clark Barwick, Peter Haine
In this short note we extend the Exodromy Theorem of arXiv:1807.03281 to a large class of stacks and higher stacks. We accomplish this by extending the Galois category construction…
Extended étale homotopy groups from profinite Galois categories
Peter J. Haine
In this note we show that the protruncated shape of a spectral -topos is a delocalization of its profinite stratified shape. This gives a way to reconstruct the extended ét…