Results 221 to 230 of about 1,689,750 (280)
Some of the next articles are maybe not open access.
Torsion Pairs in Categories of Modules over a Preadditive Category
Bulletin of the Iranian Mathematical Society, 2019It is a result of Gabriel that hereditary torsion pairs in categories of modules are in bijection with certain filters of ideals of the base ring, called Gabriel filters or Gabriel topologies.
C. Parra, Manuel Saor'in, Simone Virili
semanticscholar +1 more source
1994
Many constructions on various mathematical objects depend not just on the elements of those objects but also on the morphisms between them. Such constructions can thus be effectively formulated in the corresponding category of objects. A “topos” is a category in which a number of the most basic such constructions (product, pullback, exponential ...
Saunders Mac Lane, Ieke Moerdijk
openaire +1 more source
Many constructions on various mathematical objects depend not just on the elements of those objects but also on the morphisms between them. Such constructions can thus be effectively formulated in the corresponding category of objects. A “topos” is a category in which a number of the most basic such constructions (product, pullback, exponential ...
Saunders Mac Lane, Ieke Moerdijk
openaire +1 more source
2017
A category \(\mathcal{C}\) is formed by a class of objects \(\mathop{\mathrm{Ob}}\nolimits \mathcal{C}\) and a class of disjoint sets \(\mathop{\mathrm{Hom}}\nolimits (X,Y ) =\mathop{ \mathrm{Hom}}\nolimits _{\mathcal{C}}(X,Y )\), one set for each ordered pair of objects \(X,Y \in \mathop{\mathrm{Ob}}\nolimits \mathcal{C}\).
openaire +2 more sources
A category \(\mathcal{C}\) is formed by a class of objects \(\mathop{\mathrm{Ob}}\nolimits \mathcal{C}\) and a class of disjoint sets \(\mathop{\mathrm{Hom}}\nolimits (X,Y ) =\mathop{ \mathrm{Hom}}\nolimits _{\mathcal{C}}(X,Y )\), one set for each ordered pair of objects \(X,Y \in \mathop{\mathrm{Ob}}\nolimits \mathcal{C}\).
openaire +2 more sources
Behavioral Metrics via Functor Lifting
Foundations of Software Technology and Theoretical Computer Science, 2014We study behavioral metrics in an abstract coalgebraic setting. Given a coalgebra alpha: X -> FX in Set, where the functor F specifies the branching type, we define a framework for deriving pseudometrics on X which measure the behavioral distance of ...
Paolo Baldan +3 more
semanticscholar +1 more source
1974
This monograph concerns certain categories ℂ equipped with a full subcategory °ℂ with “small” or “finitely generated” objects. Both of these categories are entirely concrete. In particular the objects A, B, ℭ, ... are sets and the morphisms p, q, r, ... are maps.
J. N. Crossley, Anil Nerode
openaire +1 more source
This monograph concerns certain categories ℂ equipped with a full subcategory °ℂ with “small” or “finitely generated” objects. Both of these categories are entirely concrete. In particular the objects A, B, ℭ, ... are sets and the morphisms p, q, r, ... are maps.
J. N. Crossley, Anil Nerode
openaire +1 more source
Total Categories and Solid Functors
Canadian Journal of Mathematics, 1990Totality of a category as introduced by Street and Walters [17] is known to be a strong cocompleteness property (cf. also [21]) which goes far beyond ordinary (small) cocompleteness. It implies compactness in the sense of Isbell [11] and therefore hypercompleteness [7], that is: the existence of limits of all those (not necessarily small) diagrams ...
Börger, Reinhard, Tholen, Walter
openaire +1 more source
2012
In this first chapter of Part 2 we give a general, rapid introduction to the required language from category theory.
openaire +1 more source
In this first chapter of Part 2 we give a general, rapid introduction to the required language from category theory.
openaire +1 more source
, 2014
Note to the reader Introduction 1. Categories, functors and natural transformations 2. Adjoints 3. Interlude on sets 4. Representables 5. Limits 6. Adjoints, representables and limits Appendix: proof of the General Adjoint Functor Theorem Glossary of ...
T. Leinster
semanticscholar +1 more source
Note to the reader Introduction 1. Categories, functors and natural transformations 2. Adjoints 3. Interlude on sets 4. Representables 5. Limits 6. Adjoints, representables and limits Appendix: proof of the General Adjoint Functor Theorem Glossary of ...
T. Leinster
semanticscholar +1 more source
1992
Abstract As we begin to compare categories with one another we must always specify which category an object or arrow is in. We will speak of an object A of a category A, or an arrow f:B→ C of a category B.
openaire +1 more source
Abstract As we begin to compare categories with one another we must always specify which category an object or arrow is in. We will speak of an object A of a category A, or an arrow f:B→ C of a category B.
openaire +1 more source
Regular Categories and Regular Functors
Canadian Journal of Mathematics, 1974Let be a category with nice factorization-properties. If a functor G: —> which has a left-adjoint behaves nice with respect to factorizations then it can be shown quite easily that G behaves well in many other respects, especially that it lifts nice properties from into .
openaire +2 more sources