Relative extriangulated categories arising from half exact functors
نویسندگان
چکیده
Relative theories(=closed subfunctors) are considered in exact, triangulated and extriangulated categories by Dräxler-Reiten-Smalø-Solberg-Keller, Beligiannis Herschend-Liu-Nakaoka, respectively. We give a construction method of closed subfunctors from given half exact functors which contains existing constructions. Moreover, if an category has enough projective objects, then every subfunctor is obtained this construction.
منابع مشابه
Regular functors and relative realisability categories
The relative realizability toposes that Awodey, Birkedal and Scott introduced in [1] satisfy a universal property that involves regular functors to other categories. We use this universal property to define what relative realizability categories are, when based on other categories than of the topos of sets. This paper explains the property and gives a construction for relative realizability cat...
متن کاملFunctors for Alternative Categories
An attempt to define the concept of a functor covering both cases (covariant and contravariant) resulted in a structure consisting of two fields: the object map and the morphism map, the first one mapping the Cartesian squares of the set of objects rather than the set of objects. We start with an auxiliary notion of bifunction, i.e. a function mapping the Cartesian square of a set A into the Ca...
متن کاملAdjoint functors; categories in topology
In this section, we develop the some important categorical definitions and ideas which will be used throughout this paper. For a more complete treatment, the interested reader should consult either [ML-1971], [H-1970] or [M-1967]. Definition 1.1: A metacategory (which we typically denote as C or D) is a pair C = (OC,MC) where OC is considered to be the collection of objects of C and MC is consi...
متن کاملTopological Functors as Total Categories
A notion of central importance in categorical topology is that of topological functor. A faithful functor E → B is called topological if it admits cartesian liftings of all (possibly large) families of arrows; the basic example is the forgetful functor Top→ Set. A topological functor E → 1 is the same thing as a (large) complete preorder, and the general topological functor E → B is intuitively...
متن کاملOpposite Categories and Contravariant Functors
The opposite category of a category, contravariant functors and duality functors are defined. Next we state the proposition (1) the objects of C, the morphisms of C, the cod-map of C, the dom-map of C, (the composition of C),the id-map of C is a category. Let us consider C. The functor C op yielding a strict category is defined by the condition (Def. 1). (Def. 1) C op = the objects of C, the mo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2023
ISSN: ['1090-266X', '0021-8693']
DOI: https://doi.org/10.1016/j.jalgebra.2022.10.008