From 6c8379669bdf5f51b58752b190ccc26fe68440af Mon Sep 17 00:00:00 2001
From: Jim Pryor
Date: Tue, 2 Nov 2010 08:31:25 -0400
Subject: [PATCH] cat theory tweaks
Signed-off-by: Jim Pryor
---
advanced_topics/monads_in_category_theory.mdwn | 4 ++--
1 file changed, 2 insertions(+), 2 deletions(-)
diff --git a/advanced_topics/monads_in_category_theory.mdwn b/advanced_topics/monads_in_category_theory.mdwn
index 7b52c3a6..6b2eb805 100644
--- a/advanced_topics/monads_in_category_theory.mdwn
+++ b/advanced_topics/monads_in_category_theory.mdwn
@@ -63,11 +63,11 @@ A good intuitive picture of a category is as a generalized directed graph, where
Some examples of categories are:
-* Categories whose elements are sets and whose morphisms are functions between those sets. Here the source and target of a function are its domain and range, so distinct functions sharing a domain and range (e.g., sin and cos) are distinct morphisms between the same source and target elements. The identity morphism for any element/set is just the identity function for that set.
+* Categories whose elements are sets and whose morphisms are functions between those sets. Here the source and target of a function are its domain and range, so distinct functions sharing a domain and range (e.g., `sin` and `cos`) are distinct morphisms between the same source and target elements. The identity morphism for any element/set is just the identity function for that set.
* any monoid `(S,⋆,z)`

generates a category with a single element `x`; this `x` need not have any relation to `S`. The members of `S` play the role of *morphisms* of this category, rather than its elements. All of these morphisms are understood to map `x` to itself. The result of composing the morphism consisting of `s1` with the morphism `s2` is the morphism `s3`, where `s3=s1⋆s2`

. The identity morphism for the (single) category element `x` is the monoid's identity `z`.
-* a **preorder** is a structure `(S, ≤)` consisting of a reflexive, transitive, binary relation on a set `S`. It need not be connected (that is, there may be members `x`,`y` of `S` such that neither `x≤y` nor `y≤x`). It need not be anti-symmetric (that is, there may be members `s1`,`s2` of `S` such that `s1≤s2` and `s2≤s1` but `s1` and `s2` are not identical). Some examples:
+* a **preorder** is a structure `(S, ≤)`

consisting of a reflexive, transitive, binary relation on a set `S`. It need not be connected (that is, there may be members `x`,`y` of `S` such that neither `x≤y`

nor `y≤x`

). It need not be anti-symmetric (that is, there may be members `s1`,`s2` of `S` such that `s1≤s2`

and `s2≤s1`

but `s1` and `s2` are not identical). Some examples:
* sentences ordered by logical implication ("p and p" implies and is implied by "p", but these sentences are not identical; so this illustrates a pre-order without anti-symmetry)
* sets ordered by size (this illustrates it too)
--
2.11.0