In the present paper, we propose a new axiomatic approach to nonstandard analysis and its application general theory of spatial structures in terms category theory. Our framework is based on idea internal set theory, while make use an endofunctor U topos sets S together with natural transformation υ, instead as “standard”, “internal”, or “external”. Moreover, notion space called U-space, USpace...

In this paper we establish Koszul duality between dg categories and a class of curved coalgebras, generalizing the corresponding result for algebras conilpotent coalgebras. We show that normalized chain complex functor transforms Quillen equivalence quasicategories simplicial into duality. This allows us to give conceptual interpretation nerve category its adjoint. As an application, prove repr...

The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Electrophysiological potentials reveal cortical mechanisms for mental imagery, mental simulation, and grounded (embodied) cognition. Frontiers in Psychology 3:329. Grounded cognition theory proposes that cognition, including meaning, is grounded in sen-sorimotor processin...

This paper defends the doctrine that moral requirements are categorical in nature. My point of departure is John McDowell’s 1978 essay, “Are Moral Requirements Hypothetical Imperatives?”, which McDowell argues, against Philippa Foot, reasons not conditional upon agents’ desires and are, a certain sense, inescapable. After expounding view, exploring his idea “silence” other considerations discus...

Categorical geographical variables are normally classified into multinomial classes which are mutually exclusive and visualized as area-class maps. Typical categorical variables such as soil types and land cover classes are multinomial and exhibit complex interclass relationships. Interclass relationships may include three situations: cross-correlation (i.e. interdependency), neighbouring situa...