### Playing with topoi

Jul. 16th, 2017 10:12 am**timelets**

I'm now stuck on this definition.

How can I construct a simple topos to work through the definition?

Let's start with (4) and say that B represents various kinds of sports games; S - a particular game of sports, e.g. football; 1 stands for the rules; Ω - truth table to determine the nature of the game.

Looking at (5), let PB be the score; that is, each game has a score according to the official rules. B -> PB.

Let A be a bet on the outcome of a game. g: A -> PB.

What's BxA? It looks like a matrix of games and related bets. Using f: BxA -> Ω, we can determine whether the bet was legit.

What's BxPB? It looks like a matrix of games and scores. Using epsilon: BxPB -> Ω we can determine whether the score was legit.

In this topos we can say that a unique function g maps all bets to legitimate scores.

Does this make sense?

How can I construct a simple topos to work through the definition?

Let's start with (4) and say that B represents various kinds of sports games; S - a particular game of sports, e.g. football; 1 stands for the rules; Ω - truth table to determine the nature of the game.

Looking at (5), let PB be the score; that is, each game has a score according to the official rules. B -> PB.

Let A be a bet on the outcome of a game. g: A -> PB.

What's BxA? It looks like a matrix of games and related bets. Using f: BxA -> Ω, we can determine whether the bet was legit.

What's BxPB? It looks like a matrix of games and scores. Using epsilon: BxPB -> Ω we can determine whether the score was legit.

In this topos we can say that a unique function g maps all bets to legitimate scores.

Does this make sense?