Results 1 to 10 of about 10,908 (97)

Mathematical Models of Abstract Systems: Knowing abstract geometric forms [PDF]

, 2013
Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they ...
Marquis, Jean-Pierre
core   +3 more sources

Coassembly is a homotopy limit map

, 2020
We prove a claim by Williams that the coassembly map is a homotopy limit map. As an application, we show that the homotopy limit map for the coarse version of equivariant $A$-theory agrees with the coassembly map for bivariant $A$-theory that appears in ...
Malkiewich, Cary, Merling, Mona
core   +1 more source

Moduli stacks of algebraic structures and deformation theory [PDF]

, 2015
We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate diagram category ...
Yalin, Sinan
core   +1 more source

Subdivision-based homotopy equivalence of digital circles

Applied General Topology
A direct translation of the notion of homotopy equivalence from algebraic topology to digital images leads to a much more rigid definition in the context of digital topology. This results in two digital circles of different radii being not homotopic.
Samia Ashraf, Madiha Akram, Amna Amanat Ali   +2 more
doaj   +1 more source

Rigidification of algebras over multi-sorted theories

, 2009
We define the notion of a multi-sorted algebraic theory, which is a generalization of an algebraic theory in which the objects are of different "sorts." We prove a rigidification result for simplicial algebras over these theories, showing that there is a
Adámek, Badzioch, Bergner, Boardman, Borceux, Dwyer, Goerss, Hirschhorn, Hovey, Julia E Bergner, Lawvere, Mac Lane, Markl, Quillen   +13 more
core   +1 more source

Units of ring spectra and their traces in algebraic K-theory

, 2004
Let GL_1(R) be the units of a commutative ring spectrum R. In this paper we identify the composition BGL_1(R)->K(R)->THH(R)->\Omega^{\infty}(R), where K(R) is the algebraic K-theory and THH(R) the topological Hochschild homology of R.
Schlichtkrull, Christian
core   +2 more sources

The T-algebra spectral sequence: Comparisons and applications [PDF]

, 2014
In previous work with Niles Johnson the author constructed a spectral sequence for computing homotopy groups of spaces of maps between structured objects such as G-spaces and E_n-ring spectra.
Noel, Justin
core   +1 more source

The localization sequence for the algebraic K-theory of topological K-theory

, 2006
We prove a conjecture of Rognes by establishing a localization cofiber sequence of spectra, K(Z) to K(ku) to K(KU) to Sigma K(Z), for the algebraic K-theory of topological K-theory. We deduce the existence of this sequence as a consequence of a devissage
Andrew J. Blumberg, C. Ausoni, C. Ausoni, J. E. McClure, Michael A. Mandell   +4 more
core   +2 more sources

Continuous functors as a model for the equivariant stable homotopy category

, 2009
In this paper, we investigate the properties of the category of equivariant diagram spectra indexed on the category W_G of based G-spaces homeomorphic to finite G-CW-complexes for a compact Lie group G.
Andrew Blumberg, Blumberg, Boardman, Costenoble, Elmendorf, Lewis, Lewis, Mandell, May, May, May, Shimakawa, Shimakawa   +12 more
core   +1 more source

Topological Hochschild cohomology and generalized Morita equivalence [PDF]

, 2004
We explore two constructions in homotopy category with algebraic precursors in the theory of noncommutative rings and homological algebra, namely the Hochschild cohomology of ring spectra and Morita theory.
Andrew Baker, Andrey Lazarev, Generalized Morita Equivalence   +2 more
core   +3 more sources