scholarly journals Resolving by a free action linear category and applications to Hochschild-Mitchell (co)homology

2021 ◽  
Author(s):  
Claude Cibils ◽  
Eduardo N. Marcos
Keyword(s):  
Free Action ◽  
Linear Category

Minimal Event-Causal Libertarianism

2018 ◽  
Author(s):  
Christopher Evan Franklin
Keyword(s):  
Free Action ◽  
Mental States ◽  
Human Action

This chapter explains the differences between agency reductionism and nonreductionism, explains the varieties of libertarianism, and sets out the main contours of minimal event-causal libertarianism, highlighting just how minimal this theory is. Crucial to understanding how minimal event-causal libertarianism differs from other event-causal libertarian theories is understanding the location and role of indeterminism in human action, the kinds of mental states essential to causing free action, the nature of nondeterministic causation, and how the theory is constructed from compatibilist accounts. The chapter argues that libertarians must face up to both the problem of luck and the problem of enhanced control when determining the best theoretical location of indeterminism.

scholarly journals $$ T\overline{T} $$-like flows in non-linear electrodynamic theories and S-duality

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
H. Babaei-Aghbolagh ◽  
Komeil Babaei Velni ◽  
Davood Mahdavian Yekta ◽  
H. Mohammadzadeh
Keyword(s):  
Type Theory ◽  
Free Action ◽  
Momentum Tensor ◽  
Flow Equation ◽  
Supersymmetric Model ◽  
Deformation Problem ◽  
Dimensional Spacetime ◽  
Non Linear ◽  
The Relationship ◽  
Simple Integration

Abstract We investigate the $$ T\overline{T} $$ T T ¯ -like flows for non-linear electrodynamic theories in D(=2n)-dimensional spacetime. Our analysis is restricted to the deformation problem of the classical free action by employing the proposed $$ T\overline{T} $$ T T ¯ operator from a simple integration technique. We show that this flow equation is compatible with $$ T\overline{T} $$ T T ¯ deformation of a scalar field theory in D = 2 and of a non-linear Born-Infeld type theory in D = 4 dimensions. However, our computation discloses that this kind of $$ T\overline{T} $$ T T ¯ flow in higher dimensions is essentially different from deformation that has been derived from the AdS/CFT interpretations. Indeed, the gravity that may be exist as a holographic dual theory of this kind of effective Born-Infeld action is not necessarily an AdS space. As an illustrative investigation in D = 4, we shall also show that our construction for the $$ T\overline{T} $$ T T ¯ operator preserves the original SL(2, ℝ) symmetry of a non-supersymmetric Born-Infeld theory, as well as $$ \mathcal{N} $$ N = 2 supersymmetric model. It is shown that the corresponding SL(2, ℝ) invariant action fixes the relationship between the $$ T\overline{T} $$ T T ¯ operator and quadratic form of the energy-momentum tensor in D = 4.

scholarly journals Cartesian Differential Categories as Skew Enriched Categories

2021 ◽  
Author(s):  
Richard Garner ◽  
Jean-Simon Pacaud Lemay
Keyword(s):  
Linear Logic ◽  
Usual Sense ◽  
Enriched Category ◽  
Enriched Categories ◽  
Full Structure ◽  
Monoidal Closed Category ◽  
Category Of Modules ◽  
Differential Categories ◽  
Linear Category ◽  
Open Question

AbstractWe exhibit the cartesian differential categories of Blute, Cockett and Seely as a particular kind of enriched category. The base for the enrichment is the category of commutative monoids—or in a straightforward generalisation, the category of modules over a commutative rig k. However, the tensor product on this category is not the usual one, but rather a warping of it by a certain monoidal comonad Q. Thus the enrichment base is not a monoidal category in the usual sense, but rather a skew monoidal category in the sense of Szlachányi. Our first main result is that cartesian differential categories are the same as categories with finite products enriched over this skew monoidal base. The comonad Q involved is, in fact, an example of a differential modality. Differential modalities are a kind of comonad on a symmetric monoidal k-linear category with the characteristic feature that their co-Kleisli categories are cartesian differential categories. Using our first main result, we are able to prove our second one: that every small cartesian differential category admits a full, structure-preserving embedding into the cartesian differential category induced by a differential modality (in fact, a monoidal differential modality on a monoidal closed category—thus, a model of intuitionistic differential linear logic). This resolves an important open question in this area.

scholarly journals L2-BETTI NUMBERS OF DISCRETE MEASURED GROUPOIDS

2005 ◽  
Vol 15 (05n06) ◽  
pp. 1169-1188 ◽  
Author(s):  
ROMAN SAUER
Keyword(s):  
Probability Space ◽  
Betti Numbers ◽  
Free Action ◽  
Countable Group ◽  
Equivalence Relations ◽  
Dimension Theory ◽  
Discrete Groups ◽  
Type Ii ◽  
Orbit Equivalent ◽  
Definition Of

There are notions of L2-Betti numbers for discrete groups (Cheeger–Gromov, Lück), for type II1-factors (recent work of Connes-Shlyakhtenko) and for countable standard equivalence relations (Gaboriau). Whereas the first two are algebraically defined using Lück's dimension theory, Gaboriau's definition of the latter is inspired by the work of Cheeger and Gromov. In this work we give a definition of L2-Betti numbers of discrete measured groupoids that is based on Lück's dimension theory, thereby encompassing the cases of groups, equivalence relations and holonomy groupoids with an invariant measure for a complete transversal. We show that with our definition, like with Gaboriau's, the L2-Betti numbers [Formula: see text] of a countable group G coincide with the L2-Betti numbers [Formula: see text] of the orbit equivalence relation [Formula: see text] of a free action of G on a probability space. This yields a new proof of the fact the L2-Betti numbers of groups with orbit equivalent actions coincide.

Carbon Stocks of Linear Category of Trees Out Side Forest in Anantapuramu District, Andhra Pradesh, India

2016 ◽  
Vol 39 (4) ◽  
pp. 303-308
Author(s):  
G. Kavitha ◽  
S. Salamma ◽  
M. Ramesh ◽  
Mudavath Naik ◽  
M. Kumar ◽  
...  
Keyword(s):  
Basal Area ◽  
Carbon Stocks ◽  
Linear Structures ◽  
Carbon Sequestration Potential ◽  
Sequestration Potential ◽  
The Mean ◽  
Angiosperm Species ◽  
Linear Category ◽  
Total Tree ◽  
Trees Outside Forest

In the present study, carbon stocks of linear structures of trees outside forest in Anantapuramu district was estimated through sampling of 344 (0.1 ha) plots. A total of 4229 tree individuals belonging to 66 angiosperm species were enumerated in the sampled plots. The mean tree density is 122.8per ha; mean diameter at breast height 4.04 m; mean basal area 15.43 m2 ha-1.Mean volume of trees with >10 cm diameter is 15.50 m3 ha-1; mean total tree biomass is 120.81 tons ha-1.The mean carbon stock is 57.385 tons ha-1 and extrapolated biomass and carbon content for linear structures are 0.176 Mt and 0.083 Mt respectively. The carbon sequestration potential of trees outside forests of Anantapuramu district is estimated at 0.304 Mt.

Persona y libertad: lecturas desde la diversidad, la complejidad y la conflictividad

2020 ◽  
Author(s):  
Víctor Martin-Fiorino ◽  
Ignacio Miralbell ◽  
Eduardo Molina ◽  
Luis Mariano de la Maza ◽  
María Belén Tell ◽  
...  
Keyword(s):  
Free Action ◽  
The Other ◽  
Personal Dignity ◽  
The Will ◽  
Anthropological Approach ◽  
Community Environments

This book analyzes, from diverse but convergent historical and theoretical visions, the central problems of the anthropological structure of the person in relation to freedom - as the center of personal dignity - and with the possibilities and limits of free action and its conditionings. The text highlights the tension between rationality and responsibility when studying freedom from different perspectives, and as a decision of the person who responsibly practice it to the other people, from the will, experience and intersubjectivity. By the hands of authors, from Aristotle to contemporary anthropology, who are essential references, the text clarifies the origin of the choices in which freedom is expressed and allows deepening its understanding as an idea and as a content, from the complexity and conflict. The work studies fundamental aspects of the person-freedom relationship from ethics, psychology, politics, metaphysics and theology, and highlights the value of purpose, autonomy and community environments in which freedom is realized, keeping in mind an integrative anthropological approach. Finally, the argument about the centrality of the person is especially valuable in times of visions that minimize the human to consumption, production or ideology. The conclusions of this volume revalue the foundation and the possibility of free action that makes the being human responsible and committed.

Actualism and Beauty: Karl Barth's Insistence on the Auch in his Account of Divine Beauty

2013 ◽  
Vol 66 (3) ◽  
pp. 299-318 ◽  
Author(s):  
William T. Barnett
Keyword(s):  
Free Action ◽  
Necessary Condition ◽  
Theological Aesthetics ◽  
Free Love ◽  
Church Dogmatics ◽  
Doctrine Of God ◽  
Hans Urs Von Balthasar ◽  
Experience Of God ◽  
Free Dynamic ◽  
Divine Beauty

AbstractHans Urs von Balthasar claimed that Barth's Church Dogmatics demonstrates a weakening of his distinctive actualism in order to make space for ‘the concept of authentic objective form’, a point illustrated by the discourse on divine beauty in CD II/1. There Barth treats the divine being as an objective form to be contemplated, a seeming departure from Barth's privileged conceptualisation of God as personal subject whose free action humbles our theoretical gaze and graciously provides the material content for proper speech about God. Bruce McCormack has challenged von Balthasar's general thesis, arguing that no weakening has in fact taken place in the Church Dogmatics. If this is the case, what then of Barth's discourse on divine beauty? Is it consistent with his actualistic doctrine of God? Is it possible to speak of God both as a free, dynamic event and an object of beauty? Can theological aesthetics find a home within Barth's actualism? This article answers in the affirmative by demonstrating the systematic integrity between Barth's claims about divine beauty and the actualism permeating CD II/1. First, the article examines the ambiguity of Barth's specific claims about divine beauty. Barth is both enthusiastic and hesitant in speaking about divine beauty, affirming the concept yet placing careful qualifications on its use. Next, the article illustrates how the nature of these claims is anticipated by the actualism of CD II/1, specifically by (1) Barth's clear rejection of divine formlessness, (2) his argument that God's act of self-revelation in Jesus Christ implies an objective triune form for God's being and, lastly, (3) how he grounds discourse on divine beauty in the event of God's dynamic, free love. The article finally contends that the key to Barth's puzzling position on divine beauty is in understanding the precise reason why he registers beauty as a necessary but insufficient theological concept. This qualification is rooted in an important content–form, spirit–nature distinction which frames all discussion about God's being-in-act. Throughout CD II/1, objective form is a necessary condition for divine self-expression, but objectivity is always grounded in the freedom of the Spirit. Thus, the freedom-to-love at the heart of God's triune existence is the ground of our experience of God as beautiful, not any continuity with our contemplation of created forms. As such, the creative freedom animating God's triune life provides the space for, but also the limit to, theological aesthetics by imbuing divine beauty in mystery.

Totally knotted knots are prime

1982 ◽  
Vol 91 (3) ◽  
pp. 467-472
Author(s):  
J. C. Gomez-Larran¯aga
Keyword(s):  
Finite Number ◽  
Knot Theory ◽  
Piecewise Linear ◽  
Connected Sum ◽  
Higher Dimensional ◽  
The Family ◽  
Linear Category

Throughout, the word knot means a subspace of the 3-sphere S3 homeomorphic with the 1-sphere S1. Any knot can be expressed as a connected sum of a finite number of prime knots in a unique way (13), we consider the trivial knot a non-prime knot. (For higher dimensional knots, factorization and uniqueness have been studied in (1).) However given a knot it is difficult to determine if it is prime or not. We prove that totally knotted knots, see definition in §2, are prime in theorem 1, give a class of examples in theorem 2 and investigate how the last result can be applied to the conjecture that the family Y of unknotting number one knots are prime. (See problem 2 in (5).) At the end, prime tangles as defined by W. B. R. Lickerish are used to prove that in a certain family of knots, related somewhat to Y, there is just one non-prime knot: the square knot. The paper should be interpreted as being in the piecewise linear category. Standard definitions of 3-manifolds and knot theory may be found in (6) and (11) respectively.

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