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group algebra ” method to constructively adjoin formal radicals α, for α a unit in a commutative ring spectrum or an invertible object in a symmetric monoidal ∞- category . We show that this construction ...
Abstract: Lenses may be characterised as objects in the category of algebras over a monad, however they are often understood instead as morphisms, which propagate updates between systems. Working ...
Let A be a finite Hopf algebra over a commutative ring k. We show a one-to-one correspondence between the A-Galois extensions of k and certain functors from the category of A-comodules ...
generalization of [17, Corollary 6.4]: Corollary 5.5. A semisimple finite tensor category with property (4.1) is unimodular. □ 5.4 A commutative algebra in the center The object B=R(1) is an algebra in Z(C ...
concrete examples of categories , the converse is true. As we shall see, for the category of commutative C*- algebras this converse is equivalent to the classical Stone-Weierstrass theorem, and thus ...
the strictification |$\textbf{St}$| on pseudoalgebras, and Lack’s short paper (on codescent objects ) defined |$\textbf{St}$| on |$1$|-cells and |$2$|-cells. The result and its proof are truly beautiful category theory ...
. What makes this homology theory universal is this: if we write $$\iota $$ for the functor that carries a higher category to its moduli space of objects , then algebraic $$K$$-theory is initial among ...
with, we give a categorical equivalence between the category of NPc-lattices and morphisms and a category whose objects are pairs consisting of a Brouwerian algebra and a regular filter ...
coefficients has a complex root — the so-called ‘fundamental theorem of algebra ’2. The non-local nature of the homotopy category gives it a life of its own. Though in principle its objects are sets, we often ...
Abstract The main goal of this paper is to set a foundation for homotopy theory of algebraic stacks under model category theory and to show how it can be applied in various contexts. It not only ...
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