1,720,977 research outputs found
Multiplicative Structures on Algebraic K-Theory
No full textThe algebraic -theory of Waldhausen -categories is the functor corepresented by the unit object for a natural symmetric monoidal structure. We therefore regard it as the stable homotopy theory of homotopy theories. In particular, it respects all algebraic structures, and as a result, we obtain the Deligne Conjecture for this form of -theory
On exact ∞-categories and the Theorem of the Heart
Full text linkThe new homotopy theory of exact∞-categories is introduced and employed to prove a Theorem of the Heart for algebraic K-theory (in the sense of Waldhausen). This implies a new compatibility between Waldhausen KK-theory and Neeman K-theory. Additionally, it provides a new proof of the Dévissage and Localization theorems of Blumberg–Mandell, new models for the G-theory of schemes, and a proof of the invariance of G-theory under derived nil-thickenings
Spectral Mackey functors and equivariant algebraic <em>K</em>-Theory (I)
Full text linkSpectral Mackey functors are homotopy-coherent versions of ordinary Mackeyfunctors as defined by Dress. We show that they can be described as excisive functors on a suitable ∞-category, and we use this to show that universal examples of these objects are given by algebraic 퐾-theory. More importantly, we introduce the unfurling of certain families of Waldhausen ∞-categories bound together with suitable adjoint pairs of functors; this construction completely solves the homotopy coherence problem that arises when one wishes to study the algebraic 퐾-theory of such objects as spectral Mackey functors. Finally, we employ this technology to introduce fully functorial versions of 퐴-theory, upside-down 퐴-theory, and the algebraic 퐾-theory of derived stacks. We use this to givewhat we think is the first general construction of 휋ét1 -equivariant algebraic 퐾-theory for profinite étale fundamental groups. This is key to our approach to the “Mackey functor case” of a sequence of conjectures of Gunnar Carlsson.</p
On the algebraic K-theory of higher categories
Full text linkWe prove that Waldhausen K-theory, when extended to a very general class of quasicategories, can be described as a Goodwillie differential. In particular, K-theory spaces admit canonical (connective) deloopings, and the K-theory functor enjoys a simple universal property. Using this, we give new, higher categorical proofs of the Approximation, Additivity, and Fibration Theorems of Waldhausen in this context. As applications of this technology, we study the algebraic K-theory of associative rings in a wide range of homotopical contexts and of spectral Deligne–Mumford stacks
On left and right model categories and left and right Bousfield localizations
Full text linkWe verify the existence of left Bousfield localizations and of enriched left Bousfield localizations, and we prove a collection of useful technical results characterizing certain fibrations of (enriched) left Bousfield localizations. We also use such Bousfield localizations to construct a number of new model categories, including models for the homotopy limit of right Quillen presheaves, for Postnikov towers in model categories, and for presheaves valued in a symmetric monoidal model category satisfying a homotopy-coherent descent condition. We then verify the existence of right Bousfield localizations of right model categories, and we apply this to construct a model of the homotopy limit of a left Quillen presheaf as a right model category
n-relative categories: a model for the homotopy theory of n-fold homotopy theories
Full text linkWe introduce, for every integer n ≥ 1, the notion of an n-relative category and show that the category of the small n-relative categories is a model for the homotopy theory of n-fold homotopy theories, i.e., homotopy theories of… homotopy theories
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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