23 citations · 38 across the 6 of their papers we have counts for
6 papers
Geometric realisation as the Skorokhod semi-continuous path space endofunctor
Misha Gavrilovich, Konstantin Pimenov
We interpret a construction of geometric realisation by [Besser], [Grayson], and [Drinfeld] of a simplicial set as constructing a space of maps from the interval to a simplicial se…
A naive diagram-chasing approach to formalisation of tame topology
Misha Gavrilovich, Konstantin Pimenov
We rewrite classical topological definitions using the category-theoretic notation of arrows and are led to concise reformulations in terms of simplicial categories and orthogonali…
Rationally trivial quadratic spaces are locally trivial:III
Ivan Panin, Konstantin Pimenov
Let R be a regular semi-local domain containing a field such that all the residue fields are infinite. Let K be the fraction field of R. Let q be a quadratic space over R on a free…
On the relation of Voevodsky's algebraic cobordism to Quillen's K-theory
I. Panin, K. Pimenov, O. Röndigs
Quillen's algebraic K-theory is reconstructed via Voevodsky's algebraic cobordism. More precisely, for a ground field k the algebraic cobordism P^1-spectrum MGL of Voevodsky is con…
A universality theorem for Voevodsky's algebraic cobordism spectrum
I. Panin, K. Pimenov, O. Röndigs
An algebraic version of a theorem due to Quillen is proved. More precisely, for a ground field k we consider the motivic stable homotopy category SH(k) of P^1-spectra equipped with…
On Voevodsky's algebraic K-theory spectrum BGL
I. Panin, K. Pimenov, O. Röndigs
Under a certain normalization assumption we prove that the $\Pro^1$-spectrum of Voevodsky which represents algebraic -theory is unique over $\Spec(\mathbb{Z})$. F…