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Table of categories and functor properties (Topic)

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)

TABLES OF FUNCTORS AND MORPHISMS: PRESERVATION PROPERTIES

  1. monos extr.; monos reg.; monos epis; extr. epis; reg. epis
  2. topological $+ + + + + +$
  3. monadic $+ ? + \^aˆ’ \^aˆ’ \^aˆ’$
  4. reg. monadic $+ + + \^aˆ’ + +$
  5. reg. algebraic $+ + + \^aˆ’ + +$
  6. algebraic $+ + + \^aˆ’ + \^aˆ’$
  7. essentially algebraic $+ + + \^aˆ’ \^aˆ’ \^aˆ’$
  8. solid $+ + + \^aˆ’ \^aˆ’ \^aˆ’$
  9. full refl. embedding $+ + + \^aˆ’ \^aˆ’ \^aˆ’$
  10. adjoint $+ \^aˆ’ + \^aˆ’ \^aˆ’ \^aˆ’$
  11. faithful $\^aˆ’ \^aˆ’ \^aˆ’ \^aˆ’ \^aˆ’ \^aˆ’$

FUNCTORS AND MORPHISMS: REFLECTION PROPERTIES

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

TABLES OF FUNCTORS AND LIMITS

  1. creates, lifts, uniquely preserves, reflects
  2. topological $\^aˆ’ + + \^aˆ’$
  3. monadic $+ + + +$
  4. essentially algebraic $+ + + +$
  5. solid, uniquely transp. $\^aˆ’ + + \^aˆ’$
  6. adjoint $\^aˆ’ \^aˆ’ + \^aˆ’$

Functors AND COLIMITS

  1. lifts; uniquely preserves; detects:
  2. topological $+ + +$
  3. monadic $\^aˆ’ \^aˆ’ \^aˆ’$
  4. solid $\^aˆ’ \^aˆ’ +$

STABILITY PROPERTIES OF SPECIAL EPIMORPHISMS

  1. composition; pushouts; co–intersections
  2. isomorphisms $+ + +$
  3. retractions $+ \^aˆ’ \^aˆ’$
  4. reg. epis $\^aˆ’ + \^aˆ’$
  5. strict epis $\^aˆ’ + +$
  6. swell epis $+ + +$
  7. strong epis $+ + +$
  8. extr. epis $\^aˆ’ \^aˆ’ \^aˆ’$
  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, functors, T-algebras, operator, groups, topological groups, Abelian groups, objects
There are 200 references to this object.

This is version 6 of Table of categories and functor properties, born on 2010-06-05, modified 2010-06-05.
Object id is 872, canonical name is TableOfCategories.
Accessed 2847 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 )
Pending Errata and Addenda
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