Related papers: The Invariance and the General CCT Theorems

Category theory provides a collective description of many arrangements in mathematics, such as topological spaces, Banach spaces and game theory. Within this collective description, the perspective from any individual member of the…

In this paper we study the algebra of graph invariants, focusing mainly on the invariants of simple graphs. All other invariants, such as sorted eigenvalues, degree sequences and canonical permutations, belong to this algebra. In fact,…

We present the notion of "cyclic double multicategory", as a structure in which to organise multivariable adjunctions and mates. The classic example of a 2-variable adjunction is the hom/tensor/cotensor trio of functors; we generalise this…

C. Weibel and Thomason-Trobaugh proved (under some assumptions) that algebraic K-theory with coefficients is A1-homotopy invariant. In this article we generalize this result from schemes to the broad setting of dg categories. Along the way,…

In 1955 Dye proved that two von Neumann factors not of type I_2n are isomorphic (via a linear or a conjugate linear *-isomorphism) if and only if their unitary groups are isomorphic as abstract groups. We consider an analogue for…

Associating graph algebras to directed graphs leads to both covariant and contravariant functors from suitable categories of graphs to the category k-Alg of algebras and algebra homomorphisms. As both functors are often used at the same…

Let $f: X\to Y$ be a proper surjective morphism of varieties defined over an algebraically closed field of positive characteristic. We prove that if $f$ has geometrically connected fibers then the induced homomorphism of $F$-divided…

Building on the work of Gerstenhaber and Schack for presheaves of algebras, we define a Gerstenhaber-Schack complex C_GS(A) for an arbitrary prestack A, that is a pseudofunctor taking values in linear categories over a commutative ground…

This article is dedicated to the study of the normal functor in the category of smooth real vector bundles. Particularly, we focus on a symmetry phenomena which occurs after iterating two times the normal functor on a commutative square of…

Three new knot invariants are defined using cocycles of the generalized quandle homology theory that was proposed by Andruskiewitsch and Gra\~na. We specialize that theory to the case when there is a group action on the coefficients. First,…

This work studies conditions under which integral transforms induce exact functors on singularity categories between schemes that are proper over a Noetherian base scheme. A complete characterization for this behavior is provided, which…

We introduce a cohomological invariant arising from a class in nonabelian cohomology. This invariant generalizes the Dixmier-Douady class and encodes the obstruction to a C*-algebra bundle being the fixed-point algebra of a gauge action. As…

Birkhoff's variety theorem, a fundamental theorem of universal algebra, asserts that a subclass of a given algebra is definable by equations if and only if it satisfies specific closure properties. In a generalized version of this theorem,…

We show under suitable finiteness conditions that a functor between abelian categories induces a (not necessarily additive) map between their Grothendieck groups. This is related to the derived functors of Dold and Puppe, and generalizes a…

Given a symmetric monoidal stable $\infty$-category $\mathcal{C}$ and a left adjoint symmetric monoidal fiber functor to $\operatorname{Mod}_A^{\otimes}$ for some $\mathbb{E}_{\infty}$-ring $A$, one can construct a derived group scheme $G$…

Grothendieck Duality -- the theory of the twisted inverse image pseudofunctor (-)^! over a suitable category of scheme-maps -- can be developed concretely, with emphasis on explicit constructions, or abstractly, with emphasis on…

Complement-reducible graphs (or cographs) are the graphs formed from the single-vertex graph by the operations of complement and disjoint union. By combining the Johnson-Newman theorem on generalized cospectrality with the standard tools in…

Clifford theory relates the representation theory of finite groups to those of a fixed normal subgroup by means of induction and restriction, which is an adjoint pair of functors. We generalize this result to the situation of a…

A standard combinatorial construction, due to Kontsevich, associates to any A-infinity algebra with an invariant inner product, an inhomogeneous class in the cohomology of the moduli spaces of Riemann surfaces with marked points. We…

Fix a noetherian scheme S. For any flat map f: X->Y of separated essentially-finite-type perfect S-schemes we define a canonical derived-category map c(f):\H(X)->f^!\H(Y), the fundamental class of f, where \H(Z) is the (pre-)Hochschild…