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math.AT2024
There is no Cazanave's Theorem for punctured affine space
Thomas Brazelton, William Hornslien
In his thesis, Cazanave proved that the set of naive -homotopy classes of endomorphisms of the projective line admits a monoid structure whose group completion is gen…
math.AT2024
Polyhedral products in abstract and motivic homotopy theory
William Hornslien
We introduce polyhedral products in an -categorical setting. We generalize a splitting result by Bahri, Bendersky, Cohen, and Gitler that determines the stable homotopy typ…
math.AT2024
Polyhedral coproducts
Steven Amelotte, William Hornslien, Lewis Stanton
Dualising the construction of a polyhedral product, we introduce the notion of a polyhedral coproduct as a certain homotopy limit over the face poset of a simplicial complex. We be…