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.

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

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