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Table of categories and functor properties (Topic)

0.1 TABLE OF CATEGORIES

  1. (A∕K), 3K (objects over K)
  2. Ab (abelian groups)
  3. AbTop (abelian topological groups)
  4. AbTor (abelian torsion groups)
  5. Alg(1) (algebras with one unary operator)
  6. Alg(S2) (binary algebras)
  7. Alg(T) (T-algebras)
  8. Alg(S) (S-algebras)
  9. Alg(M) (M-algebras)
  10. Aut (automata)
  11. Autr (reachable automata)

0.2 TABLES OF FUNCTORS AND MORPHISMS: PRESERVATION PROPERTIES

  1. monos extr.; monos reg.; monos epis; extr. epis; reg. epis
  2. topological: + + + + + +
  3. monadic: + − + − −−
  4. reg. monadic: + + + − + +
  5. reg. algebraic: + + + − + +
  6. algebraic: + + + − + −
  7. essentially algebraic: + + + − −−
  8. solid: + + + − −−
  9. full refl. embedding: + + + − −−
  10. adjoint: + − + − −−
  11. faithful: − − − − −−

0.3 FUNCTORS AND MORPHISMS: REFLECTION PROPERTIES

  1. monos extr. monos reg. monos epis extr. epis reg. epis isos
  2. topological: + − − + − − −
  3. monadic: + − − + + − +
  4. reg. monadic: + − − + + + +
  5. reg. algebraic: + − − + + + +
  6. algebraic: + − − + + + +
  7. ess. algebraic: + − − + + − +
  8. solid: + − − + − − −
  9. full refl. emb.: + − − + + + +
  10. adjoint: − − − − −−
  11. faithful: + − − + − − −

0.4 TABLES OF FUNCTORS AND LIMITS

  1. creates, lifts, uniquely preserves, reflects
  2. topological: − + + −
  3. monadic: + + + +
  4. essentially algebraic: + + + +
  5. solid, uniquely transp.: − + + −
  6. adjoint: − − + −

0.5 FUNCTORS AND COLIMITS

  1. lifts; uniquely preserves; detects
  2. topological: + + +
  3. monadic: − − −
  4. solid: − − +

0.6 STABILITY PROPERTIES OF SPECIAL EPIMORPHISMS

  1. composition; pushouts; co–intersections
  2. isomorphisms: + + +
  3. retractions: + − −
  4. reg. epis: − + −
  5. strict epis: − + +
  6. swell epis: + + +
  7. strong epis: + + +
  8. extr. epis: − − −
  9. epis: + + +

"Table of categories and functor properties" is owned by bci1.
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Also defines:  preservation properties, epis, isos, (no title), essentially algebraic, strong epis, (no title), reflected properties, categorical properties, lifting, detects, special epimorphisms, stability properties, composotion, co-intersections, regular, monadic, adjoint properties, solid, algebraic, topological, reflection properties
Keywords:  categories, functors, categorical properties

Cross-references: retractions, isomorphisms, pushouts, composition, T-algebras, operator, topological groups
There are 245 references to this object.

This is version 7 of Table of categories and functor properties, born on 2010-06-05, modified 2026-09-07.
Object id is 872, canonical name is TableOfCategories.
Accessed 12360 times total.

Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
 02.70.-cxx (Computational techniques )
 02.90.+p (Other topics in mathematical methods in physics )
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