@tjaj Hello, if we start from a category C with finite products and a well-defined atomic topology, then the associated topos E is the topos of sets...

Grothendieck's new algebraic geometry, i.e. scheme theory, unifies algebraic geometry and algebraic number theory into one theory. As any commutative ...

@pierre-alain-jacqmin In categories of set-based models of algebraic theories, the forgetful functors of the algebraic structures respect limits whe...

@pierre-alain-jacqmin Your comment draws attention to a very intriguing paradox : On the one hand, the notion of category is symmetrical, in the s...

@posina Roos' Theorem, as stated on page 415 of SGA4 (volume 1), says that the three following conditions on a topos E are equivalent : i) The fam...

@pierre-alain-jacqmin To any small category with chosen finite limits, one can associate the set of objects of this category. More generally, for an...