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Nov
15
comment ETCS set theory: Are empty sets isomorphic?
@Svinepels that was the reason of my question. I am not very familiar with ETCS, but i would be very surprised to find out that it allows more than one empty set, if it has any pretense of mimicking the category of sets. So try to prove that there is exactly one empty set.
Nov
14
comment ETCS set theory: Are empty sets isomorphic?
is there more than one empty set?
Nov
8
comment Showing MON and CAT are equivalent categories
Mon and Cat are isomorphic or just equivalent?
Oct
28
comment Visualizing a homotopy pull back
Modern...yet Classical !?! sounds cool. Thank you
Oct
28
comment Visualizing a homotopy pull back
Welcome to Mathematics.SE! Are the notes for your course publicly availabel online?
Oct
27
comment Category of natural numbers with divisbility?
You don't want $0$ in this category. So the objects should be: the positive natural numbers $N^{+}$. Not the non-negative natural numbers as you state
Oct
27
comment Do adjoint functors really define monads?
@student I just edited a small typo. No math or meaning. Anything else what edited by someone else.
Oct
27
comment The empty function and constants
@Stefan your objection is correct. The problem stems from the fact that wikipedia is slighty wrong. Wikipedia should not write that the empty product is equal to....(using the equality sign), because the cartesian product is actually defined up to isomorphism and not by an equality. In other words: the equal signs that you see in the wikipedia section on nullary cartesian products should be replaced with isomrphism signs. To recap: $f \neq g$ so $A^{\emptyset} \neq B^{\emptyset}$ , but they are both isomorphic to singleton sets
Oct
27
revised The empty function and constants
edited small typos
Oct
27
suggested approved edit on The empty function and constants
Oct
27
answered Check a theorem about the category Set
Oct
27
comment Do adjoint functors really define monads?
@student Where exactly in Weibel are you looking at?
Oct
27
comment Do adjoint functors really define monads?
@GiorgioMossa the OP is interested in the comonad
Oct
27
comment Do adjoint functors really define monads?
Exactly! As a matter of fact, the same explanation appears in the first edition of CWM too.
Oct
27
comment Do adjoint functors really define monads?
@AlešBizjak The OP is interested in the comonad, not in the monad
Oct
27
revised Do adjoint functors really define monads?
edited small typos
Oct
27
comment Do adjoint functors really define monads?
"cotriple" is deprecated nowadays. Better use "comonad" instead. See CWM for terminology.
Oct
27
suggested approved edit on Do adjoint functors really define monads?
Oct
23
comment Rel instead of Set in a concrete category
A concrete category over Set is called a construct. There does not seem to be a special name for concrete categories over Rel
Oct
21
revised Functor whose values on morphisms are monomorphisms
edited title grammar