Modern developments in representation theory rely heavily on homological methods. This
book for advanced graduate students and researchers introduces these methods from their …

This paper surveys the recent advances concerning the relations between triangulated (or
derived) categories and their dg enhancements. We explain when some interesting …

" Ha habido muy pocas exposiciones sistemáticas de la teoría de las categorías derivadas
desde su inicio en el trabajo de Grothendieck y Verdier en la década de 1960. Este libro es …

To any well-behaved homology theory we associate a derived $\infty $-category which
encodes its Adams spectral sequence. As applications, we prove a conjecture of Franke on …

arXiv:2004.02479v1 [math.CT] 6 Apr 2020 Page 1 arXiv:2004.02479v1 [math.CT] 6 Apr 2020
EXTERNAL TRIANGULATION OF THE HOMOTOPY CATEGORY OF EXACT QUASI-CATEGORY …

For each prime p, we define at‑structure on the category \,\!S^0,0/τ-Mod_harm^b of harmonic
C-motivic left-module spectra over \,\!S^0,0/τ, whose MGL-homology has bounded Chow …

We study when the heart of at-structure in a triangulated category D with coproducts is AB5
or a Grothendieck category. If D satisfies Brown representability, at-structure has an AB5 …

We exhibit examples of triangulated categories which are neither the stable category of a
Frobenius category nor a full triangulated subcategory of the homotopy category of a stable …

Consider the Tate twist τ∈ H0, 1 (S0, 0) in the mod 2 cohomology of the motivic sphere.
After 2-completion, the motivic Adams spectral sequence realizes this element as a map τ …

Triangulated categories were introduced in the mid 1960's by JL Verdier in his thesis,
reprinted in [15]. Axioms similar to Verdier's were independently also suggested in [2] …