26 Characterizing specific "concrete" mathematical objects by abstract general properties 2011-12-18T00:52:32.497

25 Is there a universal property for Witt vectors? 2009-10-02T02:16:10.900

23 What is the universal property of normalization? 2009-10-01T03:44:02.800

23 What is the universal property of associated graded? 2009-10-10T20:09:51.923

19 Is there a "categorical" description of Grothendieck's algebra of differential operators? 2010-03-14T19:53:12.627

13 Elements in a localization - category theoretic approach 2012-01-28T21:31:36.003

12 "Albanese" schemes: When does an "initial abelian scheme" exist under a given scheme? 2009-10-26T01:17:13.010

12 Universal Property of the Smash Product (of pointed spaces) 2012-08-28T19:26:52.730

10 Completion of the rationals to the reals as an inverse limit construction? 2010-03-30T09:54:13.087

10 Adjoint Functors as Initial Objects of Some Category 2012-11-25T03:04:36.950

8 Can minimal surfaces be characterized by some universal property? 2010-01-27T23:45:44.790

8 Where does Segal's category come from? 2013-10-09T00:47:42.850

7 Universal nondegenrate map over the space of complete linear maps 2010-10-30T11:10:54.483

7 Is there a useful limit or co-limit of a diagram that has only a single object? 2017-01-05T18:11:45.240

7 The category of elements corresponding to a coend as a higher colimit 2017-09-30T19:56:44.100

6 universal property of blow up for stacks? 2013-02-06T18:33:04.530

6 "Universal embedding structures" in a general setting? 2016-08-09T17:00:05.407

5 Stable distributions for Lindeberg exchange strategy? 2011-02-11T18:47:36.597

5 Does $\text{Mat}_n(k)$ have some universal properties similar to its universal enveloping algebra? 2013-09-17T18:16:02.567

4 Characterizing nilpotents in a ring by a universal property 2010-02-03T18:56:04.450

4 universal property of stein factorization 2011-07-12T13:16:01.520

4 Are schemes pushouts of neighbourhoods and formal neighbourhoods? 2011-11-25T14:55:43.343

4 Do generalizations of adjoint functors, such as adjunctions in 2-categories, and multivariable adjunctions, have formulations in terms of something like universal morphisms? 2013-03-18T00:12:31.663

4 Left adjoint of pullback 2015-11-22T00:09:50.837

3 How Universal is the Topological $\mathbb K$-algebra $C(\Omega, \mathbb K)$? 2015-10-02T19:12:50.297

2 Analogs of universal coverings for vector bundles 2016-11-19T08:48:44.357

2 Categorical quotients for quasi-affine varieties 2017-03-08T21:02:50.100

1 When do coproducts commute with filtered projective limits? 2012-01-31T10:01:33.390

0 equality of elements in localization via universal property [unsolved!] 2009-12-28T00:02:51.573

0 universal families and maps to quotient stacks 2013-04-11T12:45:47.530

0 What is the universal property of being the maximal common subobject of two objects in a semisimple category? 2014-04-30T17:13:01.270