Conservative functor

<h2 id="examples">Examples</h2>
<p>The <a href="/facts/Forgetful_functor/onEwu6HA">forgetful functors</a> in <a href="/facts/Abstract_algebra/YNNE1CNz">algebra</a>, such as from Grp to Set, are conservative. More generally, every <a href="/facts/Monad_(category_theory)/6fX10Qrx">monadic functor</a> is conservative.<a class="footnote-ref" id="fnref:1" href="#fn:1"><sup>1</sup></a> In contrast, the forgetful functor from Top to Set is not conservative because not every <a href="/facts/Continuous_function/sKbl02pB">continuous bijection</a> is a <a href="/facts/Homeomorphism/jMfWg3Mn">homeomorphism</a>.
</p><p>Every <a href="/facts/Faithful_functor/bMM75v7e">faithful functor</a> from a <a href="/facts/Balanced_category/Kdpuyz3S">balanced category</a> is conservative.<a class="footnote-ref" id="fnref:2" href="#fn:2"><sup>2</sup></a>
</p>

<h2 id="external-links">External links</h2>
<ul><li><a href="https://ncatlab.org/nlab/show/conservative+functor">Conservative functor</a> at the <a href="/facts/NLab/lpPvRmgo"><i>n</i>Lab</a></li></ul>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Riehl, Emily (2016). Category Theory in Context. Courier Dover Publications. ISBN 048680903X. Retrieved 18 February 2017. <a href="048680903X" target="_blank">048680903X</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>Grandis, Marco (2013). Homological Algebra: In Strongly Non-Abelian Settings. World Scientific. ISBN 9814425931. Retrieved 14 January 2017. <a href="9814425931" target="_blank">9814425931</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
</ol>

Conservative functor open-in-new

Conservative functor