PlanetPhysics/Table of Categories

TABLE OF CATEGORIES

 * 1) (A / K), 3K (objects over K)
 * Ab,(Abelian groups)
 * 1) AbTop,(abelian topological groups)
 * 2) AbTor,(abelian torsion groups)
 * 3) Alg(1),(algebras with one unary operator)
 * 4) Alg(S2),(binary algebras)
 * 5) Alg(T),(T-algebras)
 * 6) Alg(S),(S-algebras)
 * 7) Alg(M),(M-algebras)
 * Aut,(automata)
 * 1) 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 $$+ ? + âˆ’ âˆ’ âˆ’$$
 * 4) reg. monadic $$+ + + âˆ’ + +$$
 * 5) reg. algebraic $$+ + + âˆ’ + +$$
 * 6) algebraic $$+ + + âˆ’ + âˆ’$$
 * 7) essentially algebraic $$+ + + âˆ’ âˆ’ âˆ’$$
 * 8) solid $$+ + + âˆ’ âˆ’ âˆ’$$
 * 9) full refl. embedding $$+ + + âˆ’ âˆ’ âˆ’$$
 * 10) adjoint $$+ âˆ’ + âˆ’ âˆ’ âˆ’$$
 * 11) faithful $$âˆ’ âˆ’ âˆ’ âˆ’ âˆ’ âˆ’$$

FUNCTORS AND MORPHISMS: REFLECTION PROPERTIES

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

TABLES OF FUNCTORS AND LIMITS

 * 1) creates, lifts, uniquely preserves, reflects
 * 2) topological $$ âˆ’ + + âˆ’$$
 * 3) monadic $$+ + + +$$
 * 4) essentially algebraic $$+ + + +$$
 * 5) solid, uniquely transp. $$âˆ’ + + âˆ’$$
 * 6) adjoint $$âˆ’ âˆ’ + âˆ’$$

Functors AND COLIMITS


 * 1) lifts; uniquely preserves; detects:
 * 2) topological $$+ + +$$
 * 3) monadic $$âˆ’ âˆ’ âˆ’$$
 * 4) solid $$âˆ’ âˆ’ +$$

STABILITY PROPERTIES OF SPECIAL EPIMORPHISMS


 * 1) \htmladdnormallink{composition {http://planetphysics.us/encyclopedia/Cod.html}; pushouts; co--intersections}
 * 2) isomorphisms $$+ + +$$
 * 3) retractions $$+ âˆ’ âˆ’$$
 * 4) reg. epis $$âˆ’ + âˆ’$$
 * 5) strict epis $$âˆ’ + +$$
 * 6) swell epis $$+ + +$$
 * 7) strong epis $$+ + +$$
 * 8) extr. epis $$âˆ’ âˆ’ âˆ’$$
 * 9) epis $$+ + +$$