PlanetPhysics/Table of Categories

TABLE OF CATEGORIES

1. (A / K), 3K ([[../TrivialGroupoid/|objects]] over K)
2. Ab,([[../TrivialGroupoid/|Abelian groups]])
3. AbTop,(abelian [[../PolishGroup/|topological groups]])
4. AbTor,(abelian torsion [[../TrivialGroupoid/|groups]])
5. Alg(1),(algebras with one unary [[../QuantumSpinNetworkFunctor2/|operator]])
6. Alg(S2),(binary algebras)
7. Alg(T),([[../CategoricalGroupRepresentation/|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 Failed to parse (syntax error): {\displaystyle + ? + − − −}
4. reg. monadic Failed to parse (syntax error): {\displaystyle + + + − + +}
5. reg. algebraic Failed to parse (syntax error): {\displaystyle + + + − + +}
6. algebraic Failed to parse (syntax error): {\displaystyle + + + − + −}
7. essentially algebraic Failed to parse (syntax error): {\displaystyle + + + − − −}
8. solid Failed to parse (syntax error): {\displaystyle + + + − − −}
9. full refl. embedding Failed to parse (syntax error): {\displaystyle + + + − − −}
10. adjoint Failed to parse (syntax error): {\displaystyle + − + − − −}
11. faithful Failed to parse (syntax error): {\displaystyle − − − − − −}

FUNCTORS AND MORPHISMS: REFLECTION PROPERTIES

1. monos extr. monos reg. monos epis extr. epis reg. epis isos
2. topological Failed to parse (syntax error): {\displaystyle + − − + − − −}
3. monadic Failed to parse (syntax error): {\displaystyle + − − + + − +}
4. reg. monadic Failed to parse (syntax error): {\displaystyle + − − + + + +}
5. reg. algebraic Failed to parse (syntax error): {\displaystyle + − − + + + +}
6. algebraic Failed to parse (syntax error): {\displaystyle + − − + + + +}
7. ess. algebraic Failed to parse (syntax error): {\displaystyle + − − + + − +}
8. solid Failed to parse (syntax error): {\displaystyle + − − + − − −}
9. full refl. emb. Failed to parse (syntax error): {\displaystyle + − − + + + +}
10. adjoint Failed to parse (syntax error): {\displaystyle − − − − − − }
11. faithful Failed to parse (syntax error): {\displaystyle + − − + − − −}

TABLES OF FUNCTORS AND LIMITS

1. creates, lifts, uniquely preserves, reflects
2. topological Failed to parse (syntax error): {\displaystyle − + + −}
3. monadic $++++$
4. essentially algebraic $++++$
5. solid, uniquely transp. Failed to parse (syntax error): {\displaystyle − + + −}
6. adjoint Failed to parse (syntax error): {\displaystyle − − + −}

[[../TrivialGroupoid/|Functors]] AND COLIMITS

1. lifts; uniquely preserves; detects:
2. topological $+++$
3. monadic Failed to parse (syntax error): {\displaystyle − − −}
4. solid Failed to parse (syntax error): {\displaystyle − − +}

STABILITY PROPERTIES OF SPECIAL EPIMORPHISMS

1. \htmladdnormallink{composition {http://planetphysics.us/encyclopedia/Cod.html}; [[../Pushout/|pushouts]]; co--intersections}
2. [[../IsomorphicObjectsUnderAnIsomorphism/|isomorphisms]] $+++$
3. [[../IsomorphicObjectsUnderAnIsomorphism/|retractions]] Failed to parse (syntax error): {\displaystyle + − −}
4. reg. epis Failed to parse (syntax error): {\displaystyle − + −}
5. strict epis Failed to parse (syntax error): {\displaystyle − + +}
6. swell epis $+++$
7. strong epis $+++$
8. extr. epis Failed to parse (syntax error): {\displaystyle − − −}
9. epis $+++$