# PlanetPhysics/Table of Categories
### TABLE OF CATEGORIES

* (A / K), 3K (objects over K)
* Ab,(Abelian groups)
* AbTop,(abelian topological groups)
* AbTor,(abelian torsion groups)
* Alg(1),(algebras with one unary operator)
* Alg(S2),(binary algebras)
* Alg(T),(T-algebras)
* Alg(S),(S-algebras)
* Alg(M),(M-algebras)
* Aut,(automata)
* Autr,(reachable automata)

### TABLES OF FUNCTORS AND MORPHISMS: PRESERVATION PROPERTIES

* monos extr.; monos reg.; monos epis; extr. epis; reg. epis
* topological $++++++$
* monadic Failed to parse (syntax error): {\displaystyle + ? + âˆ’ âˆ’ âˆ’}
* reg. monadic Failed to parse (syntax error): {\displaystyle + + + âˆ’ + +}
* reg. algebraic Failed to parse (syntax error): {\displaystyle + + + âˆ’ + +}
* algebraic Failed to parse (syntax error): {\displaystyle + + + âˆ’ + âˆ’}
* essentially algebraic Failed to parse (syntax error): {\displaystyle + + + âˆ’ âˆ’ âˆ’}
* solid Failed to parse (syntax error): {\displaystyle + + + âˆ’ âˆ’ âˆ’}
* full refl. embedding Failed to parse (syntax error): {\displaystyle + + + âˆ’ âˆ’ âˆ’}
* adjoint Failed to parse (syntax error): {\displaystyle + âˆ’ + âˆ’ âˆ’ âˆ’}
* faithful Failed to parse (syntax error): {\displaystyle âˆ’ âˆ’ âˆ’ âˆ’ âˆ’ âˆ’}

### FUNCTORS AND MORPHISMS: REFLECTION PROPERTIES

* monos extr. monos reg. monos epis extr. epis reg. epis isos
* topological Failed to parse (syntax error): {\displaystyle + âˆ’ âˆ’ + âˆ’ âˆ’ âˆ’}
* monadic Failed to parse (syntax error): {\displaystyle + âˆ’ âˆ’ + + âˆ’ +}
* reg. monadic Failed to parse (syntax error): {\displaystyle + âˆ’ âˆ’ + + + +}
* reg. algebraic Failed to parse (syntax error): {\displaystyle + âˆ’ âˆ’ + + + +}
* algebraic Failed to parse (syntax error): {\displaystyle + âˆ’ âˆ’ + + + +}
* ess. algebraic Failed to parse (syntax error): {\displaystyle + âˆ’ âˆ’ + + âˆ’ +}
* solid Failed to parse (syntax error): {\displaystyle + âˆ’ âˆ’ + âˆ’ âˆ’ âˆ’}
* full refl. emb. Failed to parse (syntax error): {\displaystyle + âˆ’ âˆ’ + + + +}
* adjoint Failed to parse (syntax error): {\displaystyle âˆ’ âˆ’ âˆ’ âˆ’ âˆ’ âˆ’ }
* faithful Failed to parse (syntax error): {\displaystyle + âˆ’ âˆ’ + âˆ’ âˆ’ âˆ’}

### TABLES OF FUNCTORS AND LIMITS

* creates, lifts, uniquely preserves, reflects
* topological Failed to parse (syntax error): {\displaystyle âˆ’ + + âˆ’}
* monadic $++++$
* essentially algebraic $++++$
* solid, uniquely transp. Failed to parse (syntax error): {\displaystyle âˆ’ + + âˆ’}
* adjoint Failed to parse (syntax error): {\displaystyle âˆ’ âˆ’ + âˆ’}
Functors AND COLIMITS
* lifts; uniquely preserves; detects:
* topological $+++$
* monadic Failed to parse (syntax error): {\displaystyle âˆ’ âˆ’ âˆ’}
* solid Failed to parse (syntax error): {\displaystyle âˆ’ âˆ’ +}
STABILITY PROPERTIES OF SPECIAL EPIMORPHISMS
* \htmladdnormallink{composition {http://planetphysics.us/encyclopedia/Cod.html}; pushouts; co--intersections}
* isomorphisms $+++$
* retractions Failed to parse (syntax error): {\displaystyle + âˆ’ âˆ’}
* reg. epis Failed to parse (syntax error): {\displaystyle âˆ’ + âˆ’}
* strict epis Failed to parse (syntax error): {\displaystyle âˆ’ + +}
* swell epis $+++$
* strong epis $+++$
* extr. epis Failed to parse (syntax error): {\displaystyle âˆ’ âˆ’ âˆ’}
* epis $+++$