On Closed Categories of Functors
نویسنده
چکیده
Brian Day Received November 7, 19~9 The purpose of the present paper is to develop in further detail the remarks, concerning the relationship of Kan functor extensions to closed structures on functor categories, made in "Enriched functor categories" | 1] §9. It is assumed that the reader is familiar with the basic results of closed category theory, including the representation theorem. Apart from some minor changes mentioned below, the terminology and notation employed are those of |i], |3], and |5].
منابع مشابه
Simplicial radditive functors
The goal of this paper is construct a framework which can be used to proof results of this kind for a wide class of closed model categories and functors between those categories. Originally I was interested in the proof that the symmetric power functors respect A-equivalences between simplicial schemes but it soon became clear that similar problems arise for other categories (such as finite cor...
متن کاملDiscrete Generalised Polynomial Functors
We study generalised polynomial functors between presheaf categories, developing their mathematical theory together with computational applications. The main theoretical contribution is the introduction of discrete generalised polynomial functors, a class that lies in between the classes of cocontinuous and finitary functors, and is closed under composition, sums, finite products, and different...
متن کاملPolynomial Functors and Polynomial Monads
We study polynomial functors over locally cartesian closed categories. After setting up the basic theory, we show how polynomial functors assemble into a double category, in fact a framed bicategory. We show that the free monad on a polynomial endofunctor is polynomial. The relationship with operads and other related notions is explored. Introduction Background. Notions of polynomial functor ha...
متن کاملThe function ring functors of pointfree topology revisited
This paper establishes two new connections between the familiar function ring functor ${mathfrak R}$ on the category ${bf CRFrm}$ of completely regular frames and the category {bf CR}${mathbf sigma}${bf Frm} of completely regular $sigma$-frames as well as their counterparts for the analogous functor ${mathfrak Z}$ on the category {bf ODFrm} of 0-dimensional frames, given by the integer-valued f...
متن کاملOn descent for coalgebras and type transformations
We find a criterion for a morphism of coalgebras over a Barr-exact category to be effective descent and determine (effective) descent morphisms for coalgebras over toposes in some cases. Also, we study some exactness properties of endofunctors of arbitrary categories in connection with natural transformations between them as well as those of functors that these transformations induce between co...
متن کامل