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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Non-abelian Derived Categories and Derived Schur and Weyl Functors
非阿贝尔派生范畴 派生舒尔 外尔函子
2023/4/13
We'll start with reviewing Quillen and Lurie's theory of non-abelian derived categories (also known as the "animation" theory). Following that, we will apply this theory to generalize the classical Sc...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Derived Grassmannians, derived Schur functors, and their applications
派生 格拉斯曼量 舒尔函子 应用
2023/4/21
In this talk, we will revisit Grothendieck's theory of Grassmannians and flag schemes and the theory of Schur and Weyl module functors studied in $GL_n$-representation theory from theperspective of de...
Monoidal Functors, Species and Hopf Algebras
bilax monoidal functor Fock functor Hopf algebra
2015/8/14
The fact that α is a morphism of lax monoidal functors is the same as (6.4) and the
coassociativity of I in (6.8). The fact that λ and ρ are morphisms of lax functors
is the same as (6.6) and the c...
In the theory of operads we consider functors of generalized symmetric powers defined by sums of coinvariant modules under actions of symmetric groups. One observes classically that the construction o...
Homotopy categories and idempotent completeness, weight structures and weight complex functors
Homotopy category idempotent completeness weight structure w-structure weight complex functor
2011/8/26
Abstract: This article provides some basic results on weight structures, weight complex functors and homotopy categories. We prove that the full subcategories K(A)^{w < n}, K(A)^{w > n}, K(A)^- and K(...
Categories of unitary representations of Banach-Lie supergroups and restriction functors
Banach–Lie supergroups unitary representations smooth vectors analytic vectors
2011/8/25
Abstract: We prove that the categories of smooth and analytic unitary representations of Banach--Lie supergroups are well-behaved under restriction functors, in the sense that the restriction of a rep...
A characterization of simplicial localization functors
characterization simplicial localization functors
2011/1/19
We characterize simplicial localization functors among relative functors from relative categories to simplicial categories as any choice of ho-motopy inverse to the delocalization functor of Dwyer and...
A generalization of The Dress construction for a Tambara functor, and polynomial Tambara functors
A generalization Dress construction Tambara functor polynomial Tambara functors
2011/1/19
For a finite group G, (semi-)Mackey functors and (semi-)Tambara functors are regarded as G-bivariant analogs of (semi-)groups and (semi-)rings respectively. In fact if G is trivial, they agree with th...
Bar complexes and extensions of classical exponential functors
Bar complexes extensions classical exponential functors
2011/1/21
We compute Ext-groups between classical exponential func-tors (i.e. symmetric, exterior or divided powers) and their Frobenius twists. Our method relies on bar constructions, and bridges these Ext-gro...
K-theory of $\lambda$-rings and tensorlike functors
K-theory of $\lambda$-rings tensorlike functors
2011/1/18
We refine the invariant on K2(A[Cpe ]/Im, (T − 1)) constructed in a previous paper to one which is an isomorphism for all -rings A.
Comparison of Cubical and Simplicial Derived Functors
Cubical Simplicial Derived Functors
2010/11/24
In this note we prove that the simplicial derived functors introduced by Tierney and Vogel [TV69] are naturally isomorphic to the cubical derived functors introduced by the author in [P09]. We also e...
On isomorphisms of certain functors for Cherednik algebras
certain functors Cherednik algebras
2010/11/8
Bezrukavnikov and Etingof introduced some functors between the categories O for rational Cherednik algebras. Namely, they defined two induction functors Ind_b, ind_\lambda and two restriction functors...
In this survey paper we give a relatively simple and coordinate free description of the WZW model as a local system whose base is the Gm-bundle associated to the determinant bundle on the moduli stack...
Simplicial Differerential Calculus, Divided Differences, and Construction of Weil Functors
divided differences differential calculus jet functor scalar extension
2010/12/6
We define a simplicial differential calculus by generalizing divided differences from the case of curves to the case of general maps, defined on general topological vector spaces, or even on modules o...