Homotopical resolutions associated to deformable adjunctions
نویسندگان
چکیده
منابع مشابه
Homotopical Resolutions Associated to Deformable Adjunctions
Given an adjunction F ⊣ G connecting reasonable categories with weak equivalences, we define a new derived bar and cobar construction associated to the adjunction. This yields homotopical models of the completion and cocompletion associated to the monad and comonad of the adjunction. We discuss applications of these resolutions to spectral sequences for derived completions and Goodwillie calcul...
متن کاملO ct 2 01 4 Derived sections and categorical resolutions in homotopical context
In (non-commutative) geometry, a categorical resolution of a (potentially singular) variety X is a full and faithful embedding of its derived category D(X) into a smooth and proper triangulated category T [11, 12]. The notion generalises the situation of rational singularities, where the geometric resolution functor F : X̃ → X induces the full and faithful functor F ∗ : D(X) → D(X̃) to the smooth...
متن کاملCategories Enriched over a Quantaloid: Isbell Adjunctions and Kan Adjunctions
Each distributor between categories enriched over a small quantaloid Q gives rise to two adjunctions between the categories of contravariant and covariant presheaves, and hence to two monads. These two adjunctions are respectively generalizations of Isbell adjunctions and Kan extensions in category theory. It is proved that these two processes are functorial with infomorphisms playing as morphi...
متن کاملHomotopical intersection theory I
We give a new approach to intersection theory. Our “cycles” are closed manifolds mapping into compact manifolds and our “intersections” are elements of a homotopy group of a certain Thom space. The results are then applied in various contexts, including fixed point, linking and disjunction problems. Our main theorems resemble those of Hatcher and Quinn [H-Q], but our proofs are fundamentally di...
متن کاملHomotopical Nilpotence of S3
In [l] Berstein and Ganea define the nilpotence of an ü-space to be the least integer » such that the »-commutator is nullhomotopic. We prove that S3 with the usual multiplication is 4 nilpotent. Let X be an ii-space. The 2-commutator c2: XXX—>X is defined by c2(x, y) =xyx~1y~1 where the multiplication and inverses are given by the ü-space structure of X. The »-commutator cn: X"-+X is defined i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2014
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2014.14.3021