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Homotopical algebra of Lie-Rinehart pairs
Damjan Pištalo
Dwyer-Kan localization at pairs of quasi-isomorphisms of the category of dg Lie-Rinehart pairs , where is a semi-free cdga over a field of characteristic zero and $M…
Pro-nilpotently extended dgca-s and SH Lie-Rinehart pairs
Damjan Pištalo
Category of pro-nilpotently extended differential graded commutative algebras is introduced. Chevalley-Eilenberg construction provides an equivalence between its certain full subca…
The Tor Spectral Sequence and Flat Morphisms in Homotopical -Geometry
Alisa Govzmann, Damjan Pištalo, Norbert Poncin
Homotopical algebraic -geometry combines aspects of homotopical algebraic geometry of Toen and Vezzosi and -geometry of Beilinson and Drinfeld. It was introduced by the paper…
A new approach to model categorical homotopy fiber sequences
Alisa Govzmann, Damjan Pištalo, Norbert Poncin
We propose a simplified definition of Quillen's fibration sequences in a pointed model category that fully captures the theory, although it is completely independent of the concept…
Indeterminacies and models of homotopy limits
Alisa Govzmann, Damjan Pištalo, Norbert Poncin
In \cite{CompTheo} we studied the indeterminacy of the value of a derived functor at an object using different definitions of a derived functor and different types of fibrant repla…
Comparison theorems for Kan, faintly universal and strongly universal derived functors
Alisa Govzmann, Damjan Pištalo, Norbert Poncin
We distinguish between faint, weak, strong and strict localizations of categories at morphism families and show that this framework captures the different types of derived functors…