3 citations · 5 across the 6 of their papers we have counts for
6 papers
Equivalences between localisations of categories provided by replacements
Sebastian Thomas
We give a characterisation of functors whose induced functor on the level of localisations is an equivalence and where the isomorphism inverse is induced by some kind of replacemen…
On the 3-arrow calculus for homotopy categories
Sebastian Thomas
We develop a localisation theory for certain categories, yielding a 3-arrow calculus: Every morphism in the localisation is represented by a diagram of length 3, and two such diagr…
On the second cohomology group of a simplicial group
Sebastian Thomas
We give an algebraic proof for the result of Eilenberg and Mac Lane that the second cohomology group of a simplicial group G can be computed as a quotient of a fibre product involv…
The third cohomology group classifies crossed module extensions
Sebastian Thomas
We give an elementary proof of the well-known fact that the third cohomology group H^3(G, M) of a group G with coefficients in an abelian G-module M is in bijection to the set Ext^…
Faithfulness of a functor of Quillen
William G. Dwyer, Andrei Radulescu-Banu, Sebastian Thomas
There exists a canonical functor from the category of fibrant objects of a model category modulo cylinder homotopy to its homotopy category. We show that this functor is faithful u…
The functors Wbar and Diag o Nerve are simplicially homotopy equivalent
Sebastian Thomas
Given a simplicial group G, there are two known classifying simplicial set constructions, the Kan classifying simplicial set Wbar G and Diag N G, where N denotes the dimensionwise…