Categories

DOI10.1007/BF01084981zbMath0402.18001OpenAlexW4211186685MaRDI QIDQ1255566

E. G. Shul'geifer, M. Sh. Tsalenko

Publication date: 1975

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01084981

zbMATH Keywords

Monad2-CategoriesClosed CategoryRelative Categories

Mathematics Subject Classification ID

Topoi (18B25) Theories (e.g., algebraic theories), structure, and semantics (18C10) Closed categories (closed monoidal and Cartesian closed categories, etc.) (18D15) Monads (= standard construction, triple or triad), algebras for monads, homology and derived functors for monads (18C15) Research exposition (monographs, survey articles) pertaining to category theory (18-02) Category theory; homological algebra (18-XX)

Cites Work

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• Coherence of adjoints, associativities, and identities
• Relative functor categories and categories of algebras
• On limit-preserving functors
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• Über Tensorprodukte in abelschen Kategorien
• Zur Theorie der azyklischen Modelle
• Homology and direct sums of countable abelian groups
• Equivalence of n-extensions
• A characterization of initial functors
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• Semivarieties and subfunctors of the identity functor
• Homology of categories and exactness of direct limits
• Composition functors and spectral sequences
• A generalization of certain homological functors
• Fractional categories
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• An example in category theory
• Some remarks on triples
• Satellites and cohomology
• On coherent algebras and strict algebras
• Simplicial resolutions and derived functors
• Properties of dense and relative adjoint functors
• Representable functors with values in arbitrary categories
• Factorizations of morphisms \(f:B\to FA\)
• Eine Bemerkung über Monaden und adjungierte Funktoren
• On generators and cogenerators
• Das Tensorprodukt als universelles Problem
• Epimorphisms and surjectivity
• On the quasivariety on convex subsets of affine spaces
• Coequalizers and free triples
• Addition von Korrespondenzen in abelschen Kategorien
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• Foncteurs exacts à gauche
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• Quasiprimitive subcategories
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• Preradicals and classes of morphisms
• Hopf algebras and Galois theory
• Filtrations, associated graded objects and completions
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• Limites in Kategorien von Relationalsystemen
• Generating and Cogenerating Structures
• Embedding of Categories
• Extensions in Certain Topological Algebraic Categories
• Bifunctors and Adjoint Pairs
• Upper Central Series in a Category.
• Coherence for categories with associativity, commutativity and distributivity
• Semiadjoint Functors and Quintuples
• Epireflection operators vs perfect morphisms and closed classes of epimorphisms
• Coalgebras, Sheaves, and Cohomology
• A note monies and epics in varieties of categories
• Identities in Categories
• Morita Theorems for Functor Categories
• Closed categories generated by commutative monads
• Note on monoidal localisation
• The category of representations of a completely 0-simple semigroup
• On Categories of Quotients
• Über Kategorien mit Involution
• MANIFOLDS IN CATEGORIES
• Aspects of topoi
• Ein assoziatives Produkt und ein assoziatives und kommutatives Coprodukt in der Kategorie der Mengen
• A Remark on the Existence of Limits in Categories
• Bilinearity and Cartesian Closed Monads.
• Direct limits of congruence systems
• Injective hulls as completions
• Grafi e strutture algebriche
• On a cotriple homology in a fibred category
• The Influence of M. H. Stone on the Origins of Category Theory
• RELATIONS IN CATEGORIES WITH PULLBACKS
• Homology and the Koszul complex
• Completions of Ordered Sets
• Sur certaines categories de couples d'applications croissantes
• An Epi-Reflector for Universal Theories
• Testing Categories and Strong Universality
• The Completion of an Abelian Category
• Une Caracterisation de la Categorie des Groupes
• On supernormal Ehresmann-Dedecker universes
• On the dualization of subdirect embeddings
• Epimorphisms and Dominions, III
• On subdirect embeddings in categories
• On the homology sequence in non-abelian homology.
• Bemerkungen über induktive Gruppoide
• Self-Equivalences and Principal Morphisms
• On the Addition of Relations in an Abelian Category
• Remarks on triples in enriched categories
• Subequalizers
• Triads in the homology of categories
• Completions in Abstract Homotopy Theory
• Relational algebras
• Über die Faktoralgebren der freien Kategorien über Grundgraphen
• An Interpolation Theorem for Adjoint Functors
• The Center of the Free Product of Distributive Lattices
• The right adjoints into the categories of relational systems
• On closed categories of functors
• An Elementary Theory of the Category of Topological Spaces
• On the duality of radical and semi-simple objects in categories
• A Note on Quasiprimitive Classes of Algebras
• Duality theory for Grothendieck categories
• Construction of biclosed categories
• Free Coalgebras in a Category of Rings
• On orderings of the system of subsets of ordered sets
• Obstructions to Liftings in Commutative Squares
• Triples and Localizations⁽¹⁾
• A Relationship between Left Exact and Representable Functors
• Extension of Algebraic Theories
• Subdirekte Produkte und konjunkte Summen.
• Funktoren in der Kategorie der lokal kompakten Moduln.
• Cosimplicial Cohomology of Coalgebras
• CATEGORIES STRUCTURALLY EQUIVALENT TO CATEGORIES OF ALGEBRAS
• Dinatural transformations
• Some remarks on free categories and free groupoids
• Coreflective Subcategories
• Injective Hulls of Certain S-Systems over a Semilattice
• Convenient categories of topological algebras
• Representable Functors and Operations on Rings
• Algebras over theories
• Structure of categories
• Categories of Functors and Adjoint Functors
• SPLITTING GROUPS AND PROJECTIVES IN VARIETIES OF GROUPS
• Lifting Inductive and Projective Limits
• Vervollständigung geordneter Kategorien
• Small subcategories and completeness
• Small Adequate Subcategories
• On Cohn's Theorem
• COMPOSITE MORPHISMS IN ABELIAN CATEGORIES
• Remarks on Decompositions of Categories
• Catégories Semi-Simples et Catégories Primitives
• Radical and semi-simplicity in categories
• Universelle Halbgruppe, Kategorien, freies Produkt
• Induction theorems for Grothendieck groups and Whitehead groups of finite groups
• Categories of semimodules: The categorical structural properties of transition systems
• Abstract representations of biological systems in supercategories
• COMMUTATOR, NILPOTENCY, AND SOLVABILITY IN CATEGORIES
• A Note on Exact Colimits
• Monomorphisms, Epimorphisms, and Pull-Backs
• An extension of the Krull-Schmidt theorem
• A Categorical setting for Determinants and Traces
• Deductive systems and categories
• On Fundamental Constructions and Adjoint Functors
• Epimorphisms and Dominions. IV
• Reflectors as Compositions of Epi-Reflectors
• Normal Completions of Small Categories
• On Characteristic Morphisms: In Memoriam Thomas Macfarland Cherry
• Zum Begriff des Normalteilers in Kategorien
• Injective Envelopes
• Kanonische Zerlegung von Funktoren
• Quasi-Invertibility in a Staircase Diagram
• Cohomology of coalgebras
• Über die Faktoralgebren von Gruppoiden
• Über die Vervollständigung von zu Gruppen gehörigen induktiven Gruppoiden
• Classification problems
• Universal coalgebra and categories of transition systems
• Categories Localement Artiniennes Sans Radical