Item 2 (015R) — The Clowder Project

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Style	Class	Font	Theorem Environments
Style 1	`book`	Alegreya Sans	`tcbthm`
Style 2	`book`	Alegreya Sans	`amsthm`
Style 3	`book`	Arno*	`amsthm`
Style 4	`book`	Computer Modern	`amsthm`

*To be replaced with Linus Romer's Elemaints when it is released.

1. The functor $F$ satisfies the following conditions:
1. (a) The functor $F$ is faithful, i.e. for each $A, B \in Obj (C)$ , the action on morphisms
  $F_{A, B} : {Hom}_{C} (A, B) \to {Hom}_{D} (F_{A}, F_{B})$
  
  of $F$ at $(A, B)$ is injective.
2. (b) For each $A, B \in Obj (C)$ , the restriction
  $F_{A, B}^{iso} : {Iso}_{C} (A, B) \to {Iso}_{D} (F_{A}, F_{B})$
  
  of the action on morphisms of $F$ at $(A, B)$ to isomorphisms is surjective.

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