isomorphism and contravariant functors [closed]

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
-1
down vote

favorite












There is some condition for contravariant functors to preserve and isomorphism.



There is some condition for contravariant functors to reflects and isomorphism.



.



Thank you.






category-theory







share|cite|improve this question













closed as unclear what you're asking by Alon Amit, Lord Shark the Unknown, Kevin Carlson, Paul Frost, user91500 Sep 1 at 10:16


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.














  • There is no question in this question.
    – Derek Elkins
    Sep 1 at 5:21














up vote
-1
down vote

favorite












There is some condition for contravariant functors to preserve and isomorphism.



There is some condition for contravariant functors to reflects and isomorphism.



.



Thank you.






category-theory







share|cite|improve this question













closed as unclear what you're asking by Alon Amit, Lord Shark the Unknown, Kevin Carlson, Paul Frost, user91500 Sep 1 at 10:16


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.














  • There is no question in this question.
    – Derek Elkins
    Sep 1 at 5:21












up vote
-1
down vote

favorite









up vote
-1
down vote

favorite











There is some condition for contravariant functors to preserve and isomorphism.



There is some condition for contravariant functors to reflects and isomorphism.



.



Thank you.






category-theory







share|cite|improve this question













There is some condition for contravariant functors to preserve and isomorphism.



There is some condition for contravariant functors to reflects and isomorphism.



.



Thank you.






category-theory




category-theory






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Sep 1 at 5:09









Tomais

954




954




closed as unclear what you're asking by Alon Amit, Lord Shark the Unknown, Kevin Carlson, Paul Frost, user91500 Sep 1 at 10:16


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.






closed as unclear what you're asking by Alon Amit, Lord Shark the Unknown, Kevin Carlson, Paul Frost, user91500 Sep 1 at 10:16


Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.













  • There is no question in this question.
    – Derek Elkins
    Sep 1 at 5:21
















  • There is no question in this question.
    – Derek Elkins
    Sep 1 at 5:21















There is no question in this question.
– Derek Elkins
Sep 1 at 5:21




There is no question in this question.
– Derek Elkins
Sep 1 at 5:21










1 Answer
1






active

oldest

votes

















up vote
1
down vote













Assuming the question is "Is there a condition for contravariant functors to preserve isomorphisms? Or reflect them?", the answer to the first is that all functors preserve isomorphism; the notion of isomorphism is self-dual, so it's not affected by contravariance.



One answer to the second is that there are two easy sufficient (but not necessary) conditions to reflect isomorphisms are A) that $F$ is full and faithful, or B) $F$ is faithful and the domain of $F$ is balanced (i.e. all morphisms that are both epimorphic and monomorphic are isomorphisms). Again, both of these conditions are self-dual, so contravariance changes nothing.






share|cite|improve this answer



























    1 Answer
    1






    active

    oldest

    votes








    1 Answer
    1






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    1
    down vote













    Assuming the question is "Is there a condition for contravariant functors to preserve isomorphisms? Or reflect them?", the answer to the first is that all functors preserve isomorphism; the notion of isomorphism is self-dual, so it's not affected by contravariance.



    One answer to the second is that there are two easy sufficient (but not necessary) conditions to reflect isomorphisms are A) that $F$ is full and faithful, or B) $F$ is faithful and the domain of $F$ is balanced (i.e. all morphisms that are both epimorphic and monomorphic are isomorphisms). Again, both of these conditions are self-dual, so contravariance changes nothing.






    share|cite|improve this answer
























      up vote
      1
      down vote













      Assuming the question is "Is there a condition for contravariant functors to preserve isomorphisms? Or reflect them?", the answer to the first is that all functors preserve isomorphism; the notion of isomorphism is self-dual, so it's not affected by contravariance.



      One answer to the second is that there are two easy sufficient (but not necessary) conditions to reflect isomorphisms are A) that $F$ is full and faithful, or B) $F$ is faithful and the domain of $F$ is balanced (i.e. all morphisms that are both epimorphic and monomorphic are isomorphisms). Again, both of these conditions are self-dual, so contravariance changes nothing.






      share|cite|improve this answer






















        up vote
        1
        down vote










        up vote
        1
        down vote









        Assuming the question is "Is there a condition for contravariant functors to preserve isomorphisms? Or reflect them?", the answer to the first is that all functors preserve isomorphism; the notion of isomorphism is self-dual, so it's not affected by contravariance.



        One answer to the second is that there are two easy sufficient (but not necessary) conditions to reflect isomorphisms are A) that $F$ is full and faithful, or B) $F$ is faithful and the domain of $F$ is balanced (i.e. all morphisms that are both epimorphic and monomorphic are isomorphisms). Again, both of these conditions are self-dual, so contravariance changes nothing.






        share|cite|improve this answer












        Assuming the question is "Is there a condition for contravariant functors to preserve isomorphisms? Or reflect them?", the answer to the first is that all functors preserve isomorphism; the notion of isomorphism is self-dual, so it's not affected by contravariance.



        One answer to the second is that there are two easy sufficient (but not necessary) conditions to reflect isomorphisms are A) that $F$ is full and faithful, or B) $F$ is faithful and the domain of $F$ is balanced (i.e. all morphisms that are both epimorphic and monomorphic are isomorphisms). Again, both of these conditions are self-dual, so contravariance changes nothing.







        share|cite|improve this answer












        share|cite|improve this answer



        share|cite|improve this answer










        answered Sep 1 at 5:41









        Malice Vidrine

        5,55921021




        5,55921021












            -

            這個網誌中的熱門文章

            How to combine Bézier curves to a surface?

            圖片
            Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite My aim is to smooth the terrain in a video game. Therefore I contrived an algorithm that makes use of Bézier curves of different orders. But this algorithm is defined in a two dimensional space for now. To shift it into the third dimension I need to somehow combine the Bézier curves. Given two curves in each two dimensions, how can I combine them to build a surface? I thought about something like a curve of a curve. Or maybe I could multiply them somehow. How can I combine them to cause the wanted behavior? Is there a common approach? In the image you can see the input, on the left, and the output, on the right, of the algorithm that works in a two dimensional space. For the real application there is a three dimensional input. The algorithm relays only on the adjacent tiles. Given these it will define the control points of the mentioned Bézier cur...
            閱讀完整內容

            Mutual Information Always Non-negative

            圖片
            Clash Royale CLAN TAG #URR8PPP up vote 10 down vote favorite 6 What is the simplest proof that mutual information is always non-negative? i.e., $I(X;Y)ge0$ probability-theory share | cite | improve this question edited Jun 17 '12 at 15:38 Cameron Buie 83.6k 7 71 154 asked Jun 17 '12 at 15:30 Omri 359 3 13 3 Convexity of the function $tmapsto tlog t$. – Did Jun 17 '12 at 15:33 In addition, the convexity properties require the coefficients in the linear combination sum 1. Then, as p(x,y) is a probability distribution, it fullfits such condition. – Francisco Javier Delgado Ceped Aug 10 at 18:44 add a comment  |  up vote 10 down vote favorite 6 What is the simplest proof that mutual information is always non-negative? i.e., $I(X;Y)ge0$ probability-theory share | cite | improve this question edited Jun 17 ...
            閱讀完整內容

            Why am i infinitely getting the same tweet with the Twitter Search API?

            圖片
            up vote 0 down vote favorite My code workes perfectly for other queries, but for one query I am infinitely getting the same tweet. I can't understand what the problem is. API call: query='Allergic asthma OR Nonallergic asthma OR Occupational asthma OR EIB OR Exercise-induced bronchoconstriction OR Nocturnal asthma OR Cough-variant asthma' new_tweets = api.search(q=searchQuery, count=100, since_id=since_id, lang='en',tweet_mode='extended') if not new_tweets: print("No more tweets found") break for tweet in new_tweets: if True: print(jsonpickle.encode(tweet._json, unpicklable=False)) my_file = open('searchTweets.txt','a') my_file.write(jsonpickle.encode(tweet._json, unpicklable=False)+'n') my_file.close() else: continue Output in file: https://pastebin.com/JmRCsTeE These are the JSONs of the same Tweet. Other queries that work: Breast cancer OR Prostate cancer OR Colon cancer OR Lung cancer Type 2 dia...
            閱讀完整內容